The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for...The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality (LMI) approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.展开更多
In this paper, we investigate the decentralized stabilization of some time-varying uncertain large-scale stochastic systems with delays under matching conditions. A type of decentralized controllers with guaranteed s...In this paper, we investigate the decentralized stabilization of some time-varying uncertain large-scale stochastic systems with delays under matching conditions. A type of decentralized controllers with guaranteed stabilization and sub-optimality are also given.展开更多
The paper is concerned with stabilization problem for a class of stochastic switching systems with time-delay in the detection of switching signal. By using binomial model,Poisson process,and Wiener process to describ...The paper is concerned with stabilization problem for a class of stochastic switching systems with time-delay in the detection of switching signal. By using binomial model,Poisson process,and Wiener process to describe time-delay, switching signal, and exogenous disturbance, respectively, the system under investigation is entirely set in a stochastic framework. The influence of the random time-delay is combined into reconstructing the switching signal of overall closed-loop system and changes the distribution property of switching points. Therefore,based on the asymptotical behaviors of Poisson processes and Wiener processes,the almost surely exponential stability conditions are established. Furthermore,a design methodology is posed for solving the stabilization control.展开更多
The problems of robust exponential stability in mean square and delayed state feedback stabilization for uncertain stochastic systems with time-varying delay are studied. By using Jensen's integral inequality and com...The problems of robust exponential stability in mean square and delayed state feedback stabilization for uncertain stochastic systems with time-varying delay are studied. By using Jensen's integral inequality and combining with the free weighting matrix approach, new delay-dependent stability conditions and delayed state feedback stabilization criteria are obtained in terms of linear matrix inequalities. Meanwhile, the proposed delayed state feedback stabilization criteria are more convenient in application than the existing ones since fewer tuning parameters are involved. Numerical examples are given to illustrate the effectiveness of the proposed methods.展开更多
This paper deals with global stabilization problem for the nonlinear systems with structural uncertainty. Based on control Lyapunov function, a sufficient and necessary condition for the globally and asymptotically st...This paper deals with global stabilization problem for the nonlinear systems with structural uncertainty. Based on control Lyapunov function, a sufficient and necessary condition for the globally and asymptotically stabilizing the equailibrium of the closed system is given. Moreovery, an almost smooth state feedback control law is constructed. The simulation shows the effectiveness of the method.展开更多
The robust exponential stability in mean square for a class of linearstochastic uncertain control systems is dealt with. For the uncertain stochastic systems, we havedesigned an optimal controller which guarantees the...The robust exponential stability in mean square for a class of linearstochastic uncertain control systems is dealt with. For the uncertain stochastic systems, we havedesigned an optimal controller which guarantees the exponential stability of the system. Actually,we employed Lyapunov function approach and the stochastic algebraic Riccati equation (SARE) to haveshown the robustness of the linear quadratic(LQ) optimal control law. And the algebraic criteria forthe exponential stability on the linear stochastic uncertain closed-loop systems are given.展开更多
This paper deals with the robust stabilization and passivity of general nonlinear systems with structural uncertainty. By using Lyapunov function, it verifies that under some conditions the robust passivity implies th...This paper deals with the robust stabilization and passivity of general nonlinear systems with structural uncertainty. By using Lyapunov function, it verifies that under some conditions the robust passivity implies the zero-state detectability, Furthermore, it also implies the robust stabilization for such nonlinear systems. We then establish a stabilization method for the nonlinear systems with structural uncertainty. The smooth state feedback law can be constructed with the solution of an equation. Finally, it is worth noting that the main contribution of the paper establishes the relation between robust passivity and feedback stabilization for the general nonlinear systems with structural uncertainty. The simulation shows the effectiveness of the method.展开更多
A new adaptive neural network(NN) output-feedback stabilization controller is investigated for a class of uncertain stochastic nonlinear strict-feedback systems with discrete and distributed time-varying delays and ...A new adaptive neural network(NN) output-feedback stabilization controller is investigated for a class of uncertain stochastic nonlinear strict-feedback systems with discrete and distributed time-varying delays and unknown nonlinear functions in both drift and diffusion terms.First,an extensional stability notion and the related criterion are introduced.Then,a nonlinear observer to estimate the unmeasurable states is designed,and a systematic backstepping procedure to design an adaptive NN output-feedback controller is proposed such that the closed-loop system is stable in probability.The effectiveness of the proposed control scheme is demonstrated via a numerical example.展开更多
This paper presents a linearized approach for the controller design of the shape of output probability density functions for general stochastic systems. A square root approximation to an output probability density fun...This paper presents a linearized approach for the controller design of the shape of output probability density functions for general stochastic systems. A square root approximation to an output probability density function is realized by a set of B-spline functions. This generally produces a nonlinear state space model for the weights of the B-spline approximation. A linearized model is therefore obtained and embedded into a performance function that measures the tracking error of the output probability density function with respect to a given distribution. By using this performance function as a Lyapunov function for the closed loop system, a feedback control input has been obtained which guarantees closed loop stability and realizes perfect tracking. The algorithm described in this paper has been tested on a simulated example and desired results have been achieved.展开更多
Stability of a class of nonlinear systems with parametric uncertainty is dealt with. This kind of systems can be viewed as feedback interconnection systems. By constructing the Lyapunov function for one of the feedbac...Stability of a class of nonlinear systems with parametric uncertainty is dealt with. This kind of systems can be viewed as feedback interconnection systems. By constructing the Lyapunov function for one of the feedback interconnection systems, the Lyapunov function for this kind of systems is obtained. Sufficient conditions of global asymptotic stability for this class of systems are deduced. The simulation shows the effectiveness of the method.展开更多
The p-moment exponential robust stability for stochastic systems with distributed delays and interval parameters is studied. By constructing the Lyapunov- Krasovskii functional and employing the decomposition techniqu...The p-moment exponential robust stability for stochastic systems with distributed delays and interval parameters is studied. By constructing the Lyapunov- Krasovskii functional and employing the decomposition technique of interval matrix and Ito's formula, the delay-dependent criteria for the p-moment exponential robust stability are obtained. Numerical examples show the validity and practicality of the presented criteria.展开更多
The problem of delay-dependent exponential stability is investigated for impulsive stochastic systems with time-varying delay. Although the exponential stability of impulsive stochastic delay systems has been discusse...The problem of delay-dependent exponential stability is investigated for impulsive stochastic systems with time-varying delay. Although the exponential stability of impulsive stochastic delay systems has been discussed by several authors, few works have been done on delay-dependent exponential stability of impulsive stochastic delay systems. Firstly, the Lyapunov-Krasovskii functional method combing the free-weighting matrix approach is applied to investigate this problem. Some delay-dependent mean square exponential stability criteria are derived in terms of linear matrix inequalities. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters and impulsive effects. The obtained results show that the system will stable if the impulses' frequency and amplitude are suitably related to the increase or decrease of the continuous flows, and impulses may be used as controllers to stabilize the underlying stochastic system. Numerical examples are given to show the effectiveness of the results.展开更多
This paper investigates the problem of event-triggered finite-time <i>H</i><sub>∞</sub> control for a class of switched stochastic systems. The main objective of this study is to design an eve...This paper investigates the problem of event-triggered finite-time <i>H</i><sub>∞</sub> control for a class of switched stochastic systems. The main objective of this study is to design an event-triggered state feedback <i>H</i><sub>∞</sub> controller such that the resulting closed-loop system is finite-time bounded and satisfies a prescribed <i>H</i><sub>∞</sub> level in some given finite-time interval. Based on stochastic differential equations theory and average dwell time approach, sufficient conditions are derived to ensure the finite-time stochastic stability with the prescribed <i>H</i><sub>∞</sub> performance for the relevant closed-loop system by employing the linear matrix inequality technique. Finally, the desired state feedback <i>H</i><sub>∞</sub> controller gain matrices can be expressed in an explicit form.展开更多
This paper investigates the problem of robust finite-time H<sub>∞</sub> filter design for Itô stochastic systems. Based on linear matrix inequalities (LMIS) techniques and stability theory of sto...This paper investigates the problem of robust finite-time H<sub>∞</sub> filter design for Itô stochastic systems. Based on linear matrix inequalities (LMIS) techniques and stability theory of stochastic differential equations, stochastic Lyapunov function method is adopted to design a finite-time H<sub>∞</sub> filter such that, for all admissible uncertainties, the filtering error system is stochastic finite-time stable (SFTS). A sufficient condition for the existence of a finite-time H<sub>∞</sub> filter for the stochastic system under consideration is achieved in terms of LMIS. Moreover, the explicit expression of the desired filter parameters is given. A numerical example is provided to illustrate the effectiveness of the proposed method.展开更多
To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno (T-S) fuzzy model is used to represent a nonlinear singular stochastic system wi...To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno (T-S) fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay. Based on the linear matrix inequality (LMI) techniques and stability theory of stochastic differential equations, a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller. The resulting closed-loop fuzzy system is robustly reliable stochastically stable, and the corresponding quadratic cost function is guaranteed to be no more than a certain upper bound for all admissible uncertainties, as well as different actuator fault cases. A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.展开更多
This paper investigates the robust stochastic stability and H∞ analysis for stochastic systems with time-varying delay and Markovian jump. By using the freeweighting matrix technique, i.e., He's technique, and a sto...This paper investigates the robust stochastic stability and H∞ analysis for stochastic systems with time-varying delay and Markovian jump. By using the freeweighting matrix technique, i.e., He's technique, and a stochastic Lyapunov-Krasovskii functional, new delay-dependent criteria in terms of linear matrix inequalities are derived for the the robust stochastic stability and the H∞ disturbance attenuation. Three numerical examples axe given. The results show that the proposed method is efficient and much less conservative than the existing results in the literature.展开更多
This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation an...This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation and introducing free weighting matrices, a new type of Lyapunov-Krasovskii functional is constructed based on linear matrix inequalities (LMIs), and some new delay-dependent criteria are obtained. These criteria include the delay-independent/rate- dependent and delay-dependent/rate-independent exponential stability criteria. These new criteria are less conservative than existing ones. Numerical examples demonstrate that these new criteria are effective and are an improvement over existing ones.展开更多
This study is concerned with the problem of finite-time H∞ filter design for uncertain discrete-time Markov Jump stochastic systems. Our attention is focused on the design of mode-dependent H∞ filter to ensure the f...This study is concerned with the problem of finite-time H∞ filter design for uncertain discrete-time Markov Jump stochastic systems. Our attention is focused on the design of mode-dependent H∞ filter to ensure the finite-time stability of the filtering error system and preserve a prescribed H∞ performance level for all admissible uncertainties. Sufficient conditions of filtering design for the system under consideration are developed and the corresponding filter parameters can be achieved in terms of linear matrix inequalities (LMI). Finally, a numerical example is provided to illustrate the validity of the proposed method.展开更多
基金supported by Research Foundation of Education Bureau of Shannxi Province, PRC(No.2010JK400)
文摘The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality (LMI) approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.
基金This project was supported by the National Natural Science Foundation of China (No. 69874015) and Natural Science Foundation of
文摘In this paper, we investigate the decentralized stabilization of some time-varying uncertain large-scale stochastic systems with delays under matching conditions. A type of decentralized controllers with guaranteed stabilization and sub-optimality are also given.
基金Sponsored by the Natural Science Foundation of Heilongjiang Province of China(Grant No.LC201428,F201429)
文摘The paper is concerned with stabilization problem for a class of stochastic switching systems with time-delay in the detection of switching signal. By using binomial model,Poisson process,and Wiener process to describe time-delay, switching signal, and exogenous disturbance, respectively, the system under investigation is entirely set in a stochastic framework. The influence of the random time-delay is combined into reconstructing the switching signal of overall closed-loop system and changes the distribution property of switching points. Therefore,based on the asymptotical behaviors of Poisson processes and Wiener processes,the almost surely exponential stability conditions are established. Furthermore,a design methodology is posed for solving the stabilization control.
基金supported by the National Natural Science Foundation of China(10971232)the Natural Science Foundation of Guangdong Province(101510090010000398351009001000002)
文摘The problems of robust exponential stability in mean square and delayed state feedback stabilization for uncertain stochastic systems with time-varying delay are studied. By using Jensen's integral inequality and combining with the free weighting matrix approach, new delay-dependent stability conditions and delayed state feedback stabilization criteria are obtained in terms of linear matrix inequalities. Meanwhile, the proposed delayed state feedback stabilization criteria are more convenient in application than the existing ones since fewer tuning parameters are involved. Numerical examples are given to illustrate the effectiveness of the proposed methods.
基金Technological Project of Fujian EducationDepartment,China(No.JA0 3 163 )
文摘This paper deals with global stabilization problem for the nonlinear systems with structural uncertainty. Based on control Lyapunov function, a sufficient and necessary condition for the globally and asymptotically stabilizing the equailibrium of the closed system is given. Moreovery, an almost smooth state feedback control law is constructed. The simulation shows the effectiveness of the method.
文摘The robust exponential stability in mean square for a class of linearstochastic uncertain control systems is dealt with. For the uncertain stochastic systems, we havedesigned an optimal controller which guarantees the exponential stability of the system. Actually,we employed Lyapunov function approach and the stochastic algebraic Riccati equation (SARE) to haveshown the robustness of the linear quadratic(LQ) optimal control law. And the algebraic criteria forthe exponential stability on the linear stochastic uncertain closed-loop systems are given.
基金Sponsored by the Natural Science of Foundation of Fujian Province(Grant No.A0510025).
文摘This paper deals with the robust stabilization and passivity of general nonlinear systems with structural uncertainty. By using Lyapunov function, it verifies that under some conditions the robust passivity implies the zero-state detectability, Furthermore, it also implies the robust stabilization for such nonlinear systems. We then establish a stabilization method for the nonlinear systems with structural uncertainty. The smooth state feedback law can be constructed with the solution of an equation. Finally, it is worth noting that the main contribution of the paper establishes the relation between robust passivity and feedback stabilization for the general nonlinear systems with structural uncertainty. The simulation shows the effectiveness of the method.
基金supported by the National Natural Science Fundation of China (6080402160974139+3 种基金61075117)the Fundamental Research Funds for the Central Universities (JY10000970001K5051070000272103676)
文摘A new adaptive neural network(NN) output-feedback stabilization controller is investigated for a class of uncertain stochastic nonlinear strict-feedback systems with discrete and distributed time-varying delays and unknown nonlinear functions in both drift and diffusion terms.First,an extensional stability notion and the related criterion are introduced.Then,a nonlinear observer to estimate the unmeasurable states is designed,and a systematic backstepping procedure to design an adaptive NN output-feedback controller is proposed such that the closed-loop system is stable in probability.The effectiveness of the proposed control scheme is demonstrated via a numerical example.
文摘This paper presents a linearized approach for the controller design of the shape of output probability density functions for general stochastic systems. A square root approximation to an output probability density function is realized by a set of B-spline functions. This generally produces a nonlinear state space model for the weights of the B-spline approximation. A linearized model is therefore obtained and embedded into a performance function that measures the tracking error of the output probability density function with respect to a given distribution. By using this performance function as a Lyapunov function for the closed loop system, a feedback control input has been obtained which guarantees closed loop stability and realizes perfect tracking. The algorithm described in this paper has been tested on a simulated example and desired results have been achieved.
基金supported by the National Natural Science Foundation of China (60774011)the Natural Science Foundation of Zhejiang Province (Y105141)
文摘Stability of a class of nonlinear systems with parametric uncertainty is dealt with. This kind of systems can be viewed as feedback interconnection systems. By constructing the Lyapunov function for one of the feedback interconnection systems, the Lyapunov function for this kind of systems is obtained. Sufficient conditions of global asymptotic stability for this class of systems are deduced. The simulation shows the effectiveness of the method.
基金supported by the National Natural Science Foundation of China (No.70473037)the Natural Science Foundation of Henan Province of China (No.0611054400)
文摘The p-moment exponential robust stability for stochastic systems with distributed delays and interval parameters is studied. By constructing the Lyapunov- Krasovskii functional and employing the decomposition technique of interval matrix and Ito's formula, the delay-dependent criteria for the p-moment exponential robust stability are obtained. Numerical examples show the validity and practicality of the presented criteria.
基金supported by the National Natural Science Foundation of China (60874114)the Fundamental Research Funds for the Central Universities, South China University of Technology (SCUT)(2009ZM0140)
文摘The problem of delay-dependent exponential stability is investigated for impulsive stochastic systems with time-varying delay. Although the exponential stability of impulsive stochastic delay systems has been discussed by several authors, few works have been done on delay-dependent exponential stability of impulsive stochastic delay systems. Firstly, the Lyapunov-Krasovskii functional method combing the free-weighting matrix approach is applied to investigate this problem. Some delay-dependent mean square exponential stability criteria are derived in terms of linear matrix inequalities. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters and impulsive effects. The obtained results show that the system will stable if the impulses' frequency and amplitude are suitably related to the increase or decrease of the continuous flows, and impulses may be used as controllers to stabilize the underlying stochastic system. Numerical examples are given to show the effectiveness of the results.
文摘This paper investigates the problem of event-triggered finite-time <i>H</i><sub>∞</sub> control for a class of switched stochastic systems. The main objective of this study is to design an event-triggered state feedback <i>H</i><sub>∞</sub> controller such that the resulting closed-loop system is finite-time bounded and satisfies a prescribed <i>H</i><sub>∞</sub> level in some given finite-time interval. Based on stochastic differential equations theory and average dwell time approach, sufficient conditions are derived to ensure the finite-time stochastic stability with the prescribed <i>H</i><sub>∞</sub> performance for the relevant closed-loop system by employing the linear matrix inequality technique. Finally, the desired state feedback <i>H</i><sub>∞</sub> controller gain matrices can be expressed in an explicit form.
文摘This paper investigates the problem of robust finite-time H<sub>∞</sub> filter design for Itô stochastic systems. Based on linear matrix inequalities (LMIS) techniques and stability theory of stochastic differential equations, stochastic Lyapunov function method is adopted to design a finite-time H<sub>∞</sub> filter such that, for all admissible uncertainties, the filtering error system is stochastic finite-time stable (SFTS). A sufficient condition for the existence of a finite-time H<sub>∞</sub> filter for the stochastic system under consideration is achieved in terms of LMIS. Moreover, the explicit expression of the desired filter parameters is given. A numerical example is provided to illustrate the effectiveness of the proposed method.
基金the National Natural Science Foundation of China (60574088,60274014).
文摘To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno (T-S) fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay. Based on the linear matrix inequality (LMI) techniques and stability theory of stochastic differential equations, a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller. The resulting closed-loop fuzzy system is robustly reliable stochastically stable, and the corresponding quadratic cost function is guaranteed to be no more than a certain upper bound for all admissible uncertainties, as well as different actuator fault cases. A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.
基金Project supported by the National Natural Science Foundation of China (No. 60874027)
文摘This paper investigates the robust stochastic stability and H∞ analysis for stochastic systems with time-varying delay and Markovian jump. By using the freeweighting matrix technique, i.e., He's technique, and a stochastic Lyapunov-Krasovskii functional, new delay-dependent criteria in terms of linear matrix inequalities are derived for the the robust stochastic stability and the H∞ disturbance attenuation. Three numerical examples axe given. The results show that the proposed method is efficient and much less conservative than the existing results in the literature.
基金Supported by National Natural Science Foundation of China (60425310, 60574014), the Doctor Subject Foundation of China (20050533015, 200805330004), the Program for New Century Excellent Talents in University (NCET-06-0679), and the Natural Science Foundation of Hunan Province (08JJ1010)
基金Supported by the Natural Science Foundation of Henan Province(061105440) Supported by the Natural Science Foundation of the Education Department of Henan Province(2008A1100150)
基金supported by the National Natural Science Foundation of China (No.60525303, 60604004, 60704009) Natural Science Foundationof Hebei Province, China (No.F2005000390, F2006000270)
文摘This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation and introducing free weighting matrices, a new type of Lyapunov-Krasovskii functional is constructed based on linear matrix inequalities (LMIs), and some new delay-dependent criteria are obtained. These criteria include the delay-independent/rate- dependent and delay-dependent/rate-independent exponential stability criteria. These new criteria are less conservative than existing ones. Numerical examples demonstrate that these new criteria are effective and are an improvement over existing ones.
文摘This study is concerned with the problem of finite-time H∞ filter design for uncertain discrete-time Markov Jump stochastic systems. Our attention is focused on the design of mode-dependent H∞ filter to ensure the finite-time stability of the filtering error system and preserve a prescribed H∞ performance level for all admissible uncertainties. Sufficient conditions of filtering design for the system under consideration are developed and the corresponding filter parameters can be achieved in terms of linear matrix inequalities (LMI). Finally, a numerical example is provided to illustrate the validity of the proposed method.