The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is propo...The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is proposed. By constructing the Lyapunov function with the error terms, the infinite time domain "min-max" optimization problems are converted into convex optimization problems solving by the linear matrix inequality (LMI), and the sufficient conditions for the existence of this control are derived. It is proved that the robust stability of the closed-loop singular systems can be guaranteed by the initial feasible solutions of the optimization problems, and the regular and the impulse-free of the singular systems are also guaranteed. A simulation example illustrates the efficiency of this method.展开更多
A linear matrix inequality (LMI)-based sliding surface design method for integral sliding mode control of uncertain time- delay systems with mismatching uncertainties is proposed. The uncertain time-delay system und...A linear matrix inequality (LMI)-based sliding surface design method for integral sliding mode control of uncertain time- delay systems with mismatching uncertainties is proposed. The uncertain time-delay system under consideration may have mis- matching norm bounded uncertainties in the state matrix as well as the input matrix, A sufficient condition for the existence of a sliding surface is given to guarantee asymptotic stability of the full order slJdJng mode dynamics. An LMI characterization of the slid- ing surface is given, together with an integral sliding mode control law guaranteeing the existence of a sliding mode from the initial time. Finally, a simulation is given to show the effectiveness of the proposed method.展开更多
Performance robustness problems via the state feedback controller are investigated for a class of uncertain nonlinear systems with time-delay in both state and control, in which the neural networks are used to model t...Performance robustness problems via the state feedback controller are investigated for a class of uncertain nonlinear systems with time-delay in both state and control, in which the neural networks are used to model the nonlinearities. By using an appropriate uncertainty description and the linear difference inclusion technique, sufficient conditions for existence of such controller are derived based on the linear matrix inequalities (LMIs). Using solutions of LMIs, a state feedback control law is proposed to stabilize the perturbed system and guarantee an upper bound of system performance, which is applicable to arbitrary time-delays.展开更多
In this paper, we study the H∞ control of time-delay linear systems either with some norm-bounded uncertainties or not with (for systems not in the scope of the nominal systems of the former ones). As linear time-de...In this paper, we study the H∞ control of time-delay linear systems either with some norm-bounded uncertainties or not with (for systems not in the scope of the nominal systems of the former ones). As linear time-delay systems are infinite dimensional in natural, some new sufficient conditions in Riccati equation form are offered, which extends current related results. We also point out a mistake appeared in a recently published paper.展开更多
The problem of fuzzy modeling for state and input time-delays systems with a class of nonlinear uncertainties by fuzzy T-S model is addressed.By using the linear matrix inequality(LMI) method, the problem of fuzzy r...The problem of fuzzy modeling for state and input time-delays systems with a class of nonlinear uncertainties by fuzzy T-S model is addressed.By using the linear matrix inequality(LMI) method, the problem of fuzzy robust H ∞ controller design for the system is studied.Assuming that the nonlinear uncertain functions in the model considered are gain-bounded, a sufficient condition for the robustly asymptotic stability of the closed-loop system is obtained via Lyapunov stability theory.By solving the LMI, a feedback control law which guarantees the robustly asymptotic stability of the closed-loop system is constructed and the effect of the disturbance input on the controlled output is ruduced to a prescribed level.展开更多
Robust predictive control algorithms were presented for polytopic uncertain linear discrete systems with time-delay subjected to actuator saturation. In the first algorithm, the parameter dependent state feedback mode...Robust predictive control algorithms were presented for polytopic uncertain linear discrete systems with time-delay subjected to actuator saturation. In the first algorithm, the parameter dependent state feedback model predictive control (MPC) law was obtained from minimizing the upper bound of the cost function subjected to several linear matrix inequality constraints. In order to reduce computation burden, a second robust MPC algorithm based on nominal performance cost was presented. The feasibility of the optimization problems guarantees that the algorithms are robustly stable. The simulation results verify the effectiveness of the proposed algorithms.展开更多
Repetitive processes are a distinct class of 2D systems of both theoretic and practical interest.The robust H-infinity control problem for uncertain stochastic time-delay linear continuous repetitive processes is inve...Repetitive processes are a distinct class of 2D systems of both theoretic and practical interest.The robust H-infinity control problem for uncertain stochastic time-delay linear continuous repetitive processes is investigated in this paper.First,sufficient conditions are proposed in terms of stochastic Lyapunov stability theory,It o differential rule and linear matrix inequality technology.The corresponding controller design is then cast into a convex optimization problem.Attention is focused on constructing an admissible controller,which guarantees that the closed-loop repetitive processes are mean-square asymptotically stable and have a prespecified H-infinity performance γ with respect to all energy-bounded input signals.A numerical example illustrates the effectiveness of the proposed design scheme.展开更多
Robust H-infinity filtering for a class of uncertain discrete-time linear systems with time delays and missing measurements is studied in this paper. The uncertain parameters are supposed to reside in a convex polytop...Robust H-infinity filtering for a class of uncertain discrete-time linear systems with time delays and missing measurements is studied in this paper. The uncertain parameters are supposed to reside in a convex polytope and the missing measurements are described by a binary switching sequence satisfying a Bernoulli distribution. Our attention is focused on the analysis and design of robust H-infinity filters such that, for all admissible parameter uncertainties and all possible missing measurements, the filtering error system is exponentially mean-square stable with a prescribed H-infinity disturbance attenuation level. A parameter-dependent approach is proposed to derive a less conservative result. Sufficient conditions are established for the existence of the desired filter in terms of certain linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of the desired filter is also provided. Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed method.展开更多
This paper investigates the issue of exponential stability for a class of uncertain linear systems with a single time-delay (or multiple time-delays). We consider that the uncertainties are the parameter disturbance a...This paper investigates the issue of exponential stability for a class of uncertain linear systems with a single time-delay (or multiple time-delays). We consider that the uncertainties are the parameter disturbance and the external disturbance, both of which are stochastic. The external disturbances involve not only the current state <em>x</em>(<em>t</em>) but also the delayed state <em>x</em>(<em>t</em> - <span style="white-space:nowrap;"><em>τ</em></span>). By means of the Lyapunov-Krasovskii functional, the sufficient conditions on exponential stability for the uncertain linear systems with a single time-delay (or multiple time-delays) are performed in the form of the linear matrix inequality (LMI). Selecting the suitable matrices <em>P</em> (or <img src="Edit_b2ad88c4-c55b-4ba5-9f0c-a3cd77848964.bmp" alt="" /> ) and <em>Q</em> (or <img src="Edit_fc454108-e7f0-490d-96ec-bc6d29b72e71.bmp" alt="" /> ) and parameter <span style="white-space:nowrap;"><em>β</em></span> (or <img src="Edit_ec124eb5-7b2c-4ade-809e-53c7cc39e9a0.bmp" alt="" /> ), we can also get the bounds of the state variables for the single time-delay (or multiple time-delays) systems. In order to stabilize the solution of the single time-delay (or multiple time-delays) systems at the equilibrium point, we designed the state feedback control. Thus, the corresponding stabilization criteria are given. Finally, Numerical simulations show that a small disturbance can make a great change to the state variables of the systems. When the feedback gain control is added, the state variables of the systems can quickly stabilize at the equilibrium point. This also shows the effectiveness of the proposed method.展开更多
The exponential passive filtering problem for a class of nonlinear Markov jump systems with uncertainties and time-delays is studied. The uncertain parameters are assumed unknown but norm bounded, and the nonlineariti...The exponential passive filtering problem for a class of nonlinear Markov jump systems with uncertainties and time-delays is studied. The uncertain parameters are assumed unknown but norm bounded, and the nonlinearities satisfy the quadratic condition. Based on the passive filtering theory, the sufficient condition for the existence of the mode-dependent passive filter is given by analyzing the reconstructed observer system. By using the appropriate Lyapnnov-Krasovskii function and applying linear matrix inequalities, the design scheme of the passive filter is derived and described as an optimization one. The presented exponential passive filter makes the error dynamic systems exponentially stochastically stable for all the admissible uncertainties, time-delays and nonlinearities, has the better abilities of state tracking and satisfies the given passive norm index. Simulation results demonstrate the validity of the proposed approach.展开更多
This paper deals with the global exponential stability problems for stochastic neutral Markov jump systems (MJSs) with uncertain parameters and multiple time-delays. The delays are respectively considered as constan...This paper deals with the global exponential stability problems for stochastic neutral Markov jump systems (MJSs) with uncertain parameters and multiple time-delays. The delays are respectively considered as constant and time varying cases, and the uncertainties are assumed to be norm bounded. By selecting appropriate Lyapunov-Krasovskii functions, it gives the sufficient condition such that the uncertain neutral MJSs are globally exponentially stochastically stable for all admissible uncertainties. The stability criteria are formulated in the form of linear matrix inequalities (LMIs), which can be easily checked in practice. Finally, two numerical examples are exploited to illustrate the effectiveness of the developed techniques.展开更多
This paper deals with the robust stability of time-delay system with time-varying uncertainties via homogeneous polynomial Lyapunov-Krasovskii functions(HPLKF). We give a sufficient condition to demonstrate that the s...This paper deals with the robust stability of time-delay system with time-varying uncertainties via homogeneous polynomial Lyapunov-Krasovskii functions(HPLKF). We give a sufficient condition to demonstrate that the system is asymptotically stable.A new class of Lyapunov-Krasovskii function is introduced, whose main feature is that the conservativeness due to uncertainties is reduced. Numerical examples illustrate the effectiveness of our method.展开更多
Some new linear matrix inequality (LMI) representations for delay-independent and delay-dependent stability conditions are obtained by introducing additional matrices and eliminating the product coupling of the system...Some new linear matrix inequality (LMI) representations for delay-independent and delay-dependent stability conditions are obtained by introducing additional matrices and eliminating the product coupling of the system matrices and the Lya-punov matrices. The results improve conservativeness of the given conditions for the analysis and the design of tune-delay systems with polytopic-type uncertainty.展开更多
The problem of robust H ∞ fuzzy state feedback control for uncertain fuzzy descriptor systems with state delay is solved. In the case that time-varying uncertainties are in all parameter matrices, sufficient conditi...The problem of robust H ∞ fuzzy state feedback control for uncertain fuzzy descriptor systems with state delay is solved. In the case that time-varying uncertainties are in all parameter matrices, sufficient conditions for the existence of fuzzy state feedback controller are presented in terms of linear matrix inequality (LMI). The proposed robust H ∞ control laws guarantee that the resulting closed-loop system is regular, impulse free, and stable with prescribed H ∞ norm bounded constraint for all admissible uncertainties. Finally, a numerical example is provided to demonstrate the validity of the proposed method.展开更多
Based on an appropriate Lyapunov function,this paper analyzes the design of a delay-dependent robust H_(∞)state feedback control,with a focus on a class of non-linear uncertainty linear time-delay systems with input ...Based on an appropriate Lyapunov function,this paper analyzes the design of a delay-dependent robust H_(∞)state feedback control,with a focus on a class of non-linear uncertainty linear time-delay systems with input delay using linear matrix inequalities.Under the condition that the nonlinear uncertain functions are gain bounded,a sufficient condition dependent on the delays of the state and input is presented for the existence of H_(∞)controller.The proposed controller not only stabilized closed-loop uncertain systems but also guaranteed a prescribed H_(∞)norm bound of closed-loop transfer matrix from the disturbance to controlled output.By solving a linear matrix inequation,we can obtain the robust H_(∞)controller.An example is given to show the effectiveness of the proposed method.展开更多
The robust H∞ control problems for stochastic fuzzy neutral Markov jump systems(MJSs) with parameters uncertainties and multiple time-delays are considered.The delays are respectively considered as constant and tim...The robust H∞ control problems for stochastic fuzzy neutral Markov jump systems(MJSs) with parameters uncertainties and multiple time-delays are considered.The delays are respectively considered as constant and time varying,and the uncertain parameters are assumed to be norm bounded.By means of Takagi-Sugeno fuzzy models,the overall closed-loop fuzzy dynamics are constructed through selected membership functions.By selecting the appropriate Lyapunov-Krasovskii functions,the sufficient condition is given such that the uncertain fuzzy neutral MJSs are stochastically stability for all admissible uncertainties and satisfies the given H∞ control index.The stability and H∞ control criteria are formulated in the form of linear matrix inequalities,which can be easily checked in practice.Practical examples illustrate the effectiveness of the developed techniques.展开更多
An adaptive sliding mode control(ASMC) method, based on fractional-order disturbance-observer(FODOB), is presented for a class of fractional-order nonlinear time-delay systems(FONTDS) with uncertainties to solve the t...An adaptive sliding mode control(ASMC) method, based on fractional-order disturbance-observer(FODOB), is presented for a class of fractional-order nonlinear time-delay systems(FONTDS) with uncertainties to solve the target output tracking problem.The external disturbances are estimated by FODOB, and the unknown internal perturbations of the system are adaptively estimated by sliding mode control(SMC). Furthermore, Gronwall's inequality approach is used to ensure that the output tracking error is uniformly bounded for FONTDS. Firstly, a fractional-order sliding mode control(FOSMC) based FODOB is proposed for a fractional-order linear time-delay system(FOLTDS). Secondly, combined with adaptive estimation, the ASMC of FONTDS is studied. Finally, a numerical example of FONTDS is used to verify the effectiveness of the proposed methods.展开更多
Discrete linear quadratic control has been efciently applied to linear systems as an optimal control.However,a robotic system is highly nonlinear,heavily coupled and uncertain.To overcome the problem,the robotic syste...Discrete linear quadratic control has been efciently applied to linear systems as an optimal control.However,a robotic system is highly nonlinear,heavily coupled and uncertain.To overcome the problem,the robotic system can be modeled as a linear discrete-time time-varying system in performing repetitive tasks.This modeling motivates us to develop an optimal repetitive control.The contribution of this paper is twofold.For the frst time,it presents discrete linear quadratic repetitive control for electrically driven robots using the mentioned model.The proposed control approach is based on the voltage control strategy.Second,uncertainty is efectively compensated by employing a robust time-delay controller.The uncertainty can include parametric uncertainty,unmodeled dynamics and external disturbances.To highlight its ability in overcoming the uncertainty,the dynamic equation of an articulated robot is introduced and used for the simulation,modeling and control purposes.Stability analysis verifes the proposed control approach and simulation results show its efectiveness.展开更多
The problem of robust stability of a class of uncertain nonlinear dynamical systems with time-delay is considered. Based on the assumption that the nominal system is stable, some sufficient conditions on robust stabil...The problem of robust stability of a class of uncertain nonlinear dynamical systems with time-delay is considered. Based on the assumption that the nominal system is stable, some sufficient conditions on robust stability of uncertain nonlinear dynamical systems with time-delay are derived. Some analytical methods and a type of Lyapunov functional are used to investigate such sufficient conditions. The results obtained in this paper are applicable to perturbed time-delay systems with unbounded time-varying delay. Some previous results are improved and a numerical example is given to demonstrate the validity of our results.展开更多
This paper investigates the problem of delaydependent robust H_(∞) state-feedback control for a class of uncertain discrete-time state-delayed T-S fuzzy systems.The state delay is assumed to be time-varying and of an...This paper investigates the problem of delaydependent robust H_(∞) state-feedback control for a class of uncertain discrete-time state-delayed T-S fuzzy systems.The state delay is assumed to be time-varying and of an interval-like type with the lower and upper bounds.The parameter uncertainties are assumed to have a structured linear-fractional form.Based on a novel fuzzy-basisdependent Lyapunov-Krasovskii functional incorporating a free-weighting matrix approach,some new delaydependent sufficient conditions for robust H_(∞) performance analysis and controller synthesis are derived in terms of linear matrix inequalities(LMIs).Numerical examples are also provided to illustrate the effectiveness of the proposed approaches.展开更多
基金supported by the National Natural Science Foundation of China(60774016).
文摘The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is proposed. By constructing the Lyapunov function with the error terms, the infinite time domain "min-max" optimization problems are converted into convex optimization problems solving by the linear matrix inequality (LMI), and the sufficient conditions for the existence of this control are derived. It is proved that the robust stability of the closed-loop singular systems can be guaranteed by the initial feasible solutions of the optimization problems, and the regular and the impulse-free of the singular systems are also guaranteed. A simulation example illustrates the efficiency of this method.
基金supported in part by the National Basic Research Program of China(973 Program)(61334)
文摘A linear matrix inequality (LMI)-based sliding surface design method for integral sliding mode control of uncertain time- delay systems with mismatching uncertainties is proposed. The uncertain time-delay system under consideration may have mis- matching norm bounded uncertainties in the state matrix as well as the input matrix, A sufficient condition for the existence of a sliding surface is given to guarantee asymptotic stability of the full order slJdJng mode dynamics. An LMI characterization of the slid- ing surface is given, together with an integral sliding mode control law guaranteeing the existence of a sliding mode from the initial time. Finally, a simulation is given to show the effectiveness of the proposed method.
基金This project was supported by the National Natural Science Foundation of China (60574001)Program for New Century Excellent Talents in University (NCET-05-0485).
文摘Performance robustness problems via the state feedback controller are investigated for a class of uncertain nonlinear systems with time-delay in both state and control, in which the neural networks are used to model the nonlinearities. By using an appropriate uncertainty description and the linear difference inclusion technique, sufficient conditions for existence of such controller are derived based on the linear matrix inequalities (LMIs). Using solutions of LMIs, a state feedback control law is proposed to stabilize the perturbed system and guarantee an upper bound of system performance, which is applicable to arbitrary time-delays.
文摘In this paper, we study the H∞ control of time-delay linear systems either with some norm-bounded uncertainties or not with (for systems not in the scope of the nominal systems of the former ones). As linear time-delay systems are infinite dimensional in natural, some new sufficient conditions in Riccati equation form are offered, which extends current related results. We also point out a mistake appeared in a recently published paper.
基金supported by the Program for Natural Science Foundation of Beijing (4062030)Young Teacher Research Foundation of North China Electric Power University
文摘The problem of fuzzy modeling for state and input time-delays systems with a class of nonlinear uncertainties by fuzzy T-S model is addressed.By using the linear matrix inequality(LMI) method, the problem of fuzzy robust H ∞ controller design for the system is studied.Assuming that the nonlinear uncertain functions in the model considered are gain-bounded, a sufficient condition for the robustly asymptotic stability of the closed-loop system is obtained via Lyapunov stability theory.By solving the LMI, a feedback control law which guarantees the robustly asymptotic stability of the closed-loop system is constructed and the effect of the disturbance input on the controlled output is ruduced to a prescribed level.
基金The National High Technology Research and Development Program of China ( No2004AA412050)
文摘Robust predictive control algorithms were presented for polytopic uncertain linear discrete systems with time-delay subjected to actuator saturation. In the first algorithm, the parameter dependent state feedback model predictive control (MPC) law was obtained from minimizing the upper bound of the cost function subjected to several linear matrix inequality constraints. In order to reduce computation burden, a second robust MPC algorithm based on nominal performance cost was presented. The feasibility of the optimization problems guarantees that the algorithms are robustly stable. The simulation results verify the effectiveness of the proposed algorithms.
基金supported by the Natural Science Foundation of Heilongjiang Province(No.F200504)
文摘Repetitive processes are a distinct class of 2D systems of both theoretic and practical interest.The robust H-infinity control problem for uncertain stochastic time-delay linear continuous repetitive processes is investigated in this paper.First,sufficient conditions are proposed in terms of stochastic Lyapunov stability theory,It o differential rule and linear matrix inequality technology.The corresponding controller design is then cast into a convex optimization problem.Attention is focused on constructing an admissible controller,which guarantees that the closed-loop repetitive processes are mean-square asymptotically stable and have a prespecified H-infinity performance γ with respect to all energy-bounded input signals.A numerical example illustrates the effectiveness of the proposed design scheme.
基金This work was supported by the National Natural Science Foundation of China(No.60574084)the National 863 Project(No.2006AA04Z428)the National 973 Program of China(No.2002CB312200).
文摘Robust H-infinity filtering for a class of uncertain discrete-time linear systems with time delays and missing measurements is studied in this paper. The uncertain parameters are supposed to reside in a convex polytope and the missing measurements are described by a binary switching sequence satisfying a Bernoulli distribution. Our attention is focused on the analysis and design of robust H-infinity filters such that, for all admissible parameter uncertainties and all possible missing measurements, the filtering error system is exponentially mean-square stable with a prescribed H-infinity disturbance attenuation level. A parameter-dependent approach is proposed to derive a less conservative result. Sufficient conditions are established for the existence of the desired filter in terms of certain linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of the desired filter is also provided. Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed method.
文摘This paper investigates the issue of exponential stability for a class of uncertain linear systems with a single time-delay (or multiple time-delays). We consider that the uncertainties are the parameter disturbance and the external disturbance, both of which are stochastic. The external disturbances involve not only the current state <em>x</em>(<em>t</em>) but also the delayed state <em>x</em>(<em>t</em> - <span style="white-space:nowrap;"><em>τ</em></span>). By means of the Lyapunov-Krasovskii functional, the sufficient conditions on exponential stability for the uncertain linear systems with a single time-delay (or multiple time-delays) are performed in the form of the linear matrix inequality (LMI). Selecting the suitable matrices <em>P</em> (or <img src="Edit_b2ad88c4-c55b-4ba5-9f0c-a3cd77848964.bmp" alt="" /> ) and <em>Q</em> (or <img src="Edit_fc454108-e7f0-490d-96ec-bc6d29b72e71.bmp" alt="" /> ) and parameter <span style="white-space:nowrap;"><em>β</em></span> (or <img src="Edit_ec124eb5-7b2c-4ade-809e-53c7cc39e9a0.bmp" alt="" /> ), we can also get the bounds of the state variables for the single time-delay (or multiple time-delays) systems. In order to stabilize the solution of the single time-delay (or multiple time-delays) systems at the equilibrium point, we designed the state feedback control. Thus, the corresponding stabilization criteria are given. Finally, Numerical simulations show that a small disturbance can make a great change to the state variables of the systems. When the feedback gain control is added, the state variables of the systems can quickly stabilize at the equilibrium point. This also shows the effectiveness of the proposed method.
基金supported partly by the National Natural Science Foundation of China(60574001)the Program for New Century Excellent Talents in University(050485)the Program for Innovative Research Team of Jiangnan University.
文摘The exponential passive filtering problem for a class of nonlinear Markov jump systems with uncertainties and time-delays is studied. The uncertain parameters are assumed unknown but norm bounded, and the nonlinearities satisfy the quadratic condition. Based on the passive filtering theory, the sufficient condition for the existence of the mode-dependent passive filter is given by analyzing the reconstructed observer system. By using the appropriate Lyapnnov-Krasovskii function and applying linear matrix inequalities, the design scheme of the passive filter is derived and described as an optimization one. The presented exponential passive filter makes the error dynamic systems exponentially stochastically stable for all the admissible uncertainties, time-delays and nonlinearities, has the better abilities of state tracking and satisfies the given passive norm index. Simulation results demonstrate the validity of the proposed approach.
基金supported by the National Natural Science Foundation of China (No.60574001)Program for New Century Excellent Talents in University (No.050485)Program for Innovative Research Team of Jiangnan University
文摘This paper deals with the global exponential stability problems for stochastic neutral Markov jump systems (MJSs) with uncertain parameters and multiple time-delays. The delays are respectively considered as constant and time varying cases, and the uncertainties are assumed to be norm bounded. By selecting appropriate Lyapunov-Krasovskii functions, it gives the sufficient condition such that the uncertain neutral MJSs are globally exponentially stochastically stable for all admissible uncertainties. The stability criteria are formulated in the form of linear matrix inequalities (LMIs), which can be easily checked in practice. Finally, two numerical examples are exploited to illustrate the effectiveness of the developed techniques.
基金supported by Major Programme of National Natural Science Foundation of China(No.11190015)National Natural Science Foundation of China(No.61374006)Graduate Student Innovation Foundation of Jiangsu Province(No.3208004904)
文摘This paper deals with the robust stability of time-delay system with time-varying uncertainties via homogeneous polynomial Lyapunov-Krasovskii functions(HPLKF). We give a sufficient condition to demonstrate that the system is asymptotically stable.A new class of Lyapunov-Krasovskii function is introduced, whose main feature is that the conservativeness due to uncertainties is reduced. Numerical examples illustrate the effectiveness of our method.
文摘Some new linear matrix inequality (LMI) representations for delay-independent and delay-dependent stability conditions are obtained by introducing additional matrices and eliminating the product coupling of the system matrices and the Lya-punov matrices. The results improve conservativeness of the given conditions for the analysis and the design of tune-delay systems with polytopic-type uncertainty.
文摘The problem of robust H ∞ fuzzy state feedback control for uncertain fuzzy descriptor systems with state delay is solved. In the case that time-varying uncertainties are in all parameter matrices, sufficient conditions for the existence of fuzzy state feedback controller are presented in terms of linear matrix inequality (LMI). The proposed robust H ∞ control laws guarantee that the resulting closed-loop system is regular, impulse free, and stable with prescribed H ∞ norm bounded constraint for all admissible uncertainties. Finally, a numerical example is provided to demonstrate the validity of the proposed method.
基金supported by the National Natural Science Foundation of China (Grant No.90405011).
文摘Based on an appropriate Lyapunov function,this paper analyzes the design of a delay-dependent robust H_(∞)state feedback control,with a focus on a class of non-linear uncertainty linear time-delay systems with input delay using linear matrix inequalities.Under the condition that the nonlinear uncertain functions are gain bounded,a sufficient condition dependent on the delays of the state and input is presented for the existence of H_(∞)controller.The proposed controller not only stabilized closed-loop uncertain systems but also guaranteed a prescribed H_(∞)norm bound of closed-loop transfer matrix from the disturbance to controlled output.By solving a linear matrix inequation,we can obtain the robust H_(∞)controller.An example is given to show the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China (6097400160904045)+2 种基金the National Natural Science Foundation of Jiangsu Province (BK2009068)the Six Projects Sponsoring Talent Summits of Jiangsu Provincethe Program for Postgraduate Scientific Research and Innovation of Jiangsu Province
文摘The robust H∞ control problems for stochastic fuzzy neutral Markov jump systems(MJSs) with parameters uncertainties and multiple time-delays are considered.The delays are respectively considered as constant and time varying,and the uncertain parameters are assumed to be norm bounded.By means of Takagi-Sugeno fuzzy models,the overall closed-loop fuzzy dynamics are constructed through selected membership functions.By selecting the appropriate Lyapunov-Krasovskii functions,the sufficient condition is given such that the uncertain fuzzy neutral MJSs are stochastically stability for all admissible uncertainties and satisfies the given H∞ control index.The stability and H∞ control criteria are formulated in the form of linear matrix inequalities,which can be easily checked in practice.Practical examples illustrate the effectiveness of the developed techniques.
基金supported by the National Natural Science Foundation of China (Grant Nos. 61573008 and 61973199)the Post-Doctoral Applied Research Projects of Qingdao (Grant No. 2015122)。
文摘An adaptive sliding mode control(ASMC) method, based on fractional-order disturbance-observer(FODOB), is presented for a class of fractional-order nonlinear time-delay systems(FONTDS) with uncertainties to solve the target output tracking problem.The external disturbances are estimated by FODOB, and the unknown internal perturbations of the system are adaptively estimated by sliding mode control(SMC). Furthermore, Gronwall's inequality approach is used to ensure that the output tracking error is uniformly bounded for FONTDS. Firstly, a fractional-order sliding mode control(FOSMC) based FODOB is proposed for a fractional-order linear time-delay system(FOLTDS). Secondly, combined with adaptive estimation, the ASMC of FONTDS is studied. Finally, a numerical example of FONTDS is used to verify the effectiveness of the proposed methods.
文摘Discrete linear quadratic control has been efciently applied to linear systems as an optimal control.However,a robotic system is highly nonlinear,heavily coupled and uncertain.To overcome the problem,the robotic system can be modeled as a linear discrete-time time-varying system in performing repetitive tasks.This modeling motivates us to develop an optimal repetitive control.The contribution of this paper is twofold.For the frst time,it presents discrete linear quadratic repetitive control for electrically driven robots using the mentioned model.The proposed control approach is based on the voltage control strategy.Second,uncertainty is efectively compensated by employing a robust time-delay controller.The uncertainty can include parametric uncertainty,unmodeled dynamics and external disturbances.To highlight its ability in overcoming the uncertainty,the dynamic equation of an articulated robot is introduced and used for the simulation,modeling and control purposes.Stability analysis verifes the proposed control approach and simulation results show its efectiveness.
基金This project is supported by National Natural Science Foundation of China (69974031) and the Key Natural Science Foundation of Hunan Province (OOJJY1009)
文摘The problem of robust stability of a class of uncertain nonlinear dynamical systems with time-delay is considered. Based on the assumption that the nominal system is stable, some sufficient conditions on robust stability of uncertain nonlinear dynamical systems with time-delay are derived. Some analytical methods and a type of Lyapunov functional are used to investigate such sufficient conditions. The results obtained in this paper are applicable to perturbed time-delay systems with unbounded time-varying delay. Some previous results are improved and a numerical example is given to demonstrate the validity of our results.
基金supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region of China under Project CityU/112907.
文摘This paper investigates the problem of delaydependent robust H_(∞) state-feedback control for a class of uncertain discrete-time state-delayed T-S fuzzy systems.The state delay is assumed to be time-varying and of an interval-like type with the lower and upper bounds.The parameter uncertainties are assumed to have a structured linear-fractional form.Based on a novel fuzzy-basisdependent Lyapunov-Krasovskii functional incorporating a free-weighting matrix approach,some new delaydependent sufficient conditions for robust H_(∞) performance analysis and controller synthesis are derived in terms of linear matrix inequalities(LMIs).Numerical examples are also provided to illustrate the effectiveness of the proposed approaches.