This paper presents a robust H∞ output feedback control approach for structural systems with uncertainties in model parameters by using available acceleration measurements and proposes conditions for the existence of...This paper presents a robust H∞ output feedback control approach for structural systems with uncertainties in model parameters by using available acceleration measurements and proposes conditions for the existence of such a robust output feedback controller. The uncertainties of structural stiffness, damping and mass parameters are assumed to be norm-bounded. The proposed control approach is formulated within the framework of linear matrix inequalities, for which existing convex optimization techniques, such as the LM1 toolbox in MATLAB, can be used effectively and conveniently. To illustrate the effectiveness of the proposed robust H∞ strategy, a six-story building was subjected both to the 1940 E1 Centro earthquake record and to a suddenly applied Kanai-Tajimi filtered white noise random excitation. The results show that the proposed robust H∞ controller provides satisfactory results with or without variation of the structural stiffness, damping and mass parameters.展开更多
In this paper, global robust stability of uncertain stochastic recurrent neural networks with Markovian jumping parameters is considered. A novel Linear matrix inequal- ity(LMI) based stability criterion is obtained...In this paper, global robust stability of uncertain stochastic recurrent neural networks with Markovian jumping parameters is considered. A novel Linear matrix inequal- ity(LMI) based stability criterion is obtained to guarantee the asymptotic stability of uncertain stochastic recurrent neural networks with Markovian jumping parameters. The results are derived by using the Lyapunov functional technique, Lipchitz condition and S-procuture. Finally, numerical examples are given to demonstrate the correctness of the theoretical results. Our results are also compared with results discussed in [31] and [34] to show the effectiveness and conservativeness.展开更多
The global asymptotical stability for a class of stochastic delayed neural networks (SDNNs) with Maxkovian jumping parameters is considered. By applying Lyapunov functional method and Ito's differential rule, new d...The global asymptotical stability for a class of stochastic delayed neural networks (SDNNs) with Maxkovian jumping parameters is considered. By applying Lyapunov functional method and Ito's differential rule, new delay-dependent stability conditions are derived. All results are expressed in terms of linear matrix inequality (LMI), and a numerical example is presented to illustrate the correctness and less conservativeness of the proposed method.展开更多
The problem of how to identify the piecewise affine system is studied in this paper, where this considered piecewise affine system is a special nonlinear system. The reason why it is not easy to identify this piecewis...The problem of how to identify the piecewise affine system is studied in this paper, where this considered piecewise affine system is a special nonlinear system. The reason why it is not easy to identify this piecewise affine system is that each separated region and each unknown parameter vector are all needed to be determined simultaneously. Then, firstly, in order to achieve the identification goal, a multi-class classification process is proposed to determine each separated region. As the proposed multi-class classification process is the same with the classical data clustering strategy, the multi-class classification process can combine the first order algorithm of convex optimization, while achieving the goal of the classification process. Secondly, a zonotope parameter identification algorithm is used to construct a set, which contains the unknown parameter vector. In this zonotope parameter identification algorithm, the strict probabilistic description about the external noise is relaxed, and each unknown parameter vector is also identified. Furthermore, this constructed set is consistent with the measured output and the given bound corresponding to the noise. Thirdly, a sufficient condition about guaranteeing our derived zonotope not growing unbounded with iterations is formulated as an explicit linear matrix inequality. Finally, the effectiveness of this zonotope parameter identification algorithm is proven through a simulation example.展开更多
The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional ...The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional approach combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system; next, the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are developed. The results are given in terms of linear matrix inequalities (LMIs), which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme.展开更多
The separation of the Lyapunov matrices and system matrices plays an important role when one uses parameter-dependent Lyapunov functional handling systems with polytopic type uncertainties. The delay-dependent robust ...The separation of the Lyapunov matrices and system matrices plays an important role when one uses parameter-dependent Lyapunov functional handling systems with polytopic type uncertainties. The delay-dependent robust stability problem for systems with polytopic type uncertainties is discussed by using parameter-dependent Lyapunov functional. The derivative term in the derivative of Lyapunov functional is reserved and the free weighting matrices are employed to express the relationship between die terms in the system equation such that the Lyapunov matrices are not involved in any product terms with the system matrices. In addition, the relationships between the terms in the Leibniz Newton formula are also described by some free weighting matrices and some delay-dependent stability conditions are derived. Numerical examples demonstrate that the proposed criteria are more effective than the previous results.展开更多
In this paper, the robust output feedback cruise control for high-speed train movement with uncertain parameters is investigated. The dynamic of a high-speed train is modeled by a cascade of cars connected by flexible...In this paper, the robust output feedback cruise control for high-speed train movement with uncertain parameters is investigated. The dynamic of a high-speed train is modeled by a cascade of cars connected by flexible couplers, which is subject to rolling mechanical resistance, aerodynamic drag and wind gust. Based on Lyapunov's stability theory, the sufficient condition for the existence of the robust output feedback cruise control law is given in terms of linear matrix inequalities(LMIs), under which the high-speed train tracks the desired speed, the relative spring displacement between the two neighboring cars is stable at the equilibrium state, and meanwhile a small prescribed H∞ disturbance attenuation level is guaranteed. One numerical example is given to illustrate the effectiveness of the proposed methods.展开更多
In this paper, we have improved delay-dependent stability criteria for recurrent neural networks with a delay varying over a range and Markovian jumping parameters. The criteria improve over some previous ones in that...In this paper, we have improved delay-dependent stability criteria for recurrent neural networks with a delay varying over a range and Markovian jumping parameters. The criteria improve over some previous ones in that they have fewer matrix variables yet less conservatism. In addition, a numerical example is provided to illustrate the applicability of the result using the linear matrix inequality toolbox in MATLAB.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
The robust guaranteed cost filtering problem for a dass of linear uncertain stochastic systems with time delays is investigated. The system under study involves time delays, jumping parameters and Brownian motions. Th...The robust guaranteed cost filtering problem for a dass of linear uncertain stochastic systems with time delays is investigated. The system under study involves time delays, jumping parameters and Brownian motions. The transition of the jumping parameters in systems is governed by a finite-state Markov process. The objective is to design linear memoryless filters such that for all uncertainties, the resulting augmented system is robust stochastically stable independent of delays and satisfies the proposed guaranteed cost performance. Based on stability theory in stochastic differential equations, a sufficient condition on the existence of robust guaranteed cost filters is derived. Robust guaranteed cost filters are designed in terms of linear matrix inequalities. A convex optimization problem with LMI constraints is formulated to design the suboptimal guaranteed cost filters.展开更多
This paper presents an approach in designing a robust controller for vehicle suspensions considering changes in vehicle inertial properties. A four-degree-of-freedom half-car model with active suspension is studied in...This paper presents an approach in designing a robust controller for vehicle suspensions considering changes in vehicle inertial properties. A four-degree-of-freedom half-car model with active suspension is studied in this paper, and three main performance requirements are considered. Among these requirements, the ride comfort performance is optimized by minimizing the Ho~ norm of the transfer function from the road disturbance to the sprung mass acceleration, while the road holding performance and the suspension deflection limitation are guaranteed by constraining the generalized H2 (GH2) norms of the transfer functions from the road disturbance to the dynamic tyre load and the suspension deflection to be less than their hard limits, respectively. At the same time, the controller saturation problem is considered by constraining its peak response output to be less than a given limit using the GH2 norm as well. By solving the finite number of linear matrix inequalities (LMIs) with the minimization optimization procedure, the controller gains, which are dependent on the time-varying inertial parameters, can be obtained. Numerical simulations on both frequency and bump responses show that the designed parameter-dependent controller can achieve better active suspension performance compared with the passive suspension in spite of the variations of inertial parameters.展开更多
The problem of robust L 1 filtering with pole constraint in a disk for linear continuous polytopic uncertain systems is discussed. The attention is focused on design a linear asymptotically stable filter such that th...The problem of robust L 1 filtering with pole constraint in a disk for linear continuous polytopic uncertain systems is discussed. The attention is focused on design a linear asymptotically stable filter such that the filtering error system remains robustly stable, and has a L 1 performance constraint and pole constraint in a disk. The new robust L 1 performance criteria and regional pole placement condition are obtained via parameter-dependent Lyapunov functions method. Upon the proposed multiobjective performance criteria and by means of LMI technique, both full-order and reduced-order robust L 1 filter with suitable dynamic behavior can be obtained from the solution of convex optimization problems. Compared with earlier result in the quadratic framework, this approach turns out to be less conservative. The efficiency of the proposed technique is demonstrated by a numerical example.展开更多
This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties. A new and simple method is presented to directly decouple the Lyapunov matrix ...This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties. A new and simple method is presented to directly decouple the Lyapunov matrix and the system dynamic matrix. Combining this method with the parameter-dependent Lyapunov function approach yields new criteria that include some existing ones as special cases. A numerical example illustrates the improvement over the existing ones.展开更多
Feedback control problems for linear periodic systems (LPSs) with interval- type parameter uncertainties are studied in the discrete-time domain. First, the stability analysis and stabilization problems are addresse...Feedback control problems for linear periodic systems (LPSs) with interval- type parameter uncertainties are studied in the discrete-time domain. First, the stability analysis and stabilization problems are addressed. Conditions based on the linear matrices inequality (LMI) for the asymptotical stability and state feedback stabilization, respec-tively, are given. Problems of L2-gain analysis and control synthesis are studied. For the L2-gain analysis problem, we obtain an LMI-based condition such that the autonomous uncertain LPS is asymptotically stable and has an L2-gain smaller than a positive scalar γ. For the control synthesis problem, we derive an LMI-based condition to build a state feedback controller ensuring that the closed-loop system is asymptotically stable and has an L2-gain smaller than the positive scalar γ. All the conditions are necessary and sufficient.展开更多
The stability and stabilization of a class of nonlinear discrete time delayed systems(NDTDS) with time-varying delay and norm-bounded nonlinearity are investigated. Based on discrete time Lyapunov–Krasovskii function...The stability and stabilization of a class of nonlinear discrete time delayed systems(NDTDS) with time-varying delay and norm-bounded nonlinearity are investigated. Based on discrete time Lyapunov–Krasovskii functional method, a sufficient delaydependent condition for asymptotic stability of nonlinear systems is offered. Then, this condition is used to design a new efficient delayed state feedback controller(DSFC) for stabilization of such systems. These conditions are in the linear matrix inequality(LMI) framework. Illustrative examples confirm the improvement of the proposed approach over the similar cases. Furthermore, the obtained stability and stabilization conditions will be extended to uncertain discrete time delayed systems(UDTDS) with polytopic parameter uncertainties and also with norm-bounded parameter uncertainties.展开更多
This paper deals with the robust guaranteed cost observer with guaranteed cost performance for a class of linear uncertain jump systems with state delay.The transition of the jumping parameters in systems is governed ...This paper deals with the robust guaranteed cost observer with guaranteed cost performance for a class of linear uncertain jump systems with state delay.The transition of the jumping parameters in systems is governed by a finite-state Markov process.Based on the stability theory in stochastic differential equations,a sufficient condition on the existence of the proposed robust guaranteed cost observer is derived.Robust guaranteed cost observers are designed in terms of a set of linear coupled matrix inequalities.A convex optimization problem with LMI constraints is formulated to design the suboptimal guaranteed cost observers.展开更多
This paper proposes new sufficient conditions for the exponential stability and stabilization.of linear uncertain polytopic time-delay systems. The conditions for exponential stability are expressed in terms of Kharit...This paper proposes new sufficient conditions for the exponential stability and stabilization.of linear uncertain polytopic time-delay systems. The conditions for exponential stability are expressed in terms of Kharitonov-type linear matrix inequalities (LMIs) and we develop control design methods based on LMIs for solving stabilization problem. Our method consists of a combination of the LMI approach and the use of parameter-dependent Lyapunov functionals, which allows to compute simultaneously the two bounds that characterize the exponetial stability rate of the solution. Numerical examples illustrating the conditions are given.展开更多
基金Supported by the Natural Science Foundation of Hunan Province (07JJ6112), the Construct Program of the Key Discipline in Hunan Province (control theory and control engineering), and Scientific Research Fund of Hunan Provincial Education Department (04A012, 07A015)
基金National Natural Science Foundation of China Under Grant No. 50608012 and No.10472023The Cardiff Advanced Chinese Engineering Centre
文摘This paper presents a robust H∞ output feedback control approach for structural systems with uncertainties in model parameters by using available acceleration measurements and proposes conditions for the existence of such a robust output feedback controller. The uncertainties of structural stiffness, damping and mass parameters are assumed to be norm-bounded. The proposed control approach is formulated within the framework of linear matrix inequalities, for which existing convex optimization techniques, such as the LM1 toolbox in MATLAB, can be used effectively and conveniently. To illustrate the effectiveness of the proposed robust H∞ strategy, a six-story building was subjected both to the 1940 E1 Centro earthquake record and to a suddenly applied Kanai-Tajimi filtered white noise random excitation. The results show that the proposed robust H∞ controller provides satisfactory results with or without variation of the structural stiffness, damping and mass parameters.
基金supported by NBHM project grant No.2/48(10)/2011-RD-II/865
文摘In this paper, global robust stability of uncertain stochastic recurrent neural networks with Markovian jumping parameters is considered. A novel Linear matrix inequal- ity(LMI) based stability criterion is obtained to guarantee the asymptotic stability of uncertain stochastic recurrent neural networks with Markovian jumping parameters. The results are derived by using the Lyapunov functional technique, Lipchitz condition and S-procuture. Finally, numerical examples are given to demonstrate the correctness of the theoretical results. Our results are also compared with results discussed in [31] and [34] to show the effectiveness and conservativeness.
基金supported by the National Natural Science Foundation of China(60874114).
文摘The global asymptotical stability for a class of stochastic delayed neural networks (SDNNs) with Maxkovian jumping parameters is considered. By applying Lyapunov functional method and Ito's differential rule, new delay-dependent stability conditions are derived. All results are expressed in terms of linear matrix inequality (LMI), and a numerical example is presented to illustrate the correctness and less conservativeness of the proposed method.
文摘The problem of how to identify the piecewise affine system is studied in this paper, where this considered piecewise affine system is a special nonlinear system. The reason why it is not easy to identify this piecewise affine system is that each separated region and each unknown parameter vector are all needed to be determined simultaneously. Then, firstly, in order to achieve the identification goal, a multi-class classification process is proposed to determine each separated region. As the proposed multi-class classification process is the same with the classical data clustering strategy, the multi-class classification process can combine the first order algorithm of convex optimization, while achieving the goal of the classification process. Secondly, a zonotope parameter identification algorithm is used to construct a set, which contains the unknown parameter vector. In this zonotope parameter identification algorithm, the strict probabilistic description about the external noise is relaxed, and each unknown parameter vector is also identified. Furthermore, this constructed set is consistent with the measured output and the given bound corresponding to the noise. Thirdly, a sufficient condition about guaranteeing our derived zonotope not growing unbounded with iterations is formulated as an explicit linear matrix inequality. Finally, the effectiveness of this zonotope parameter identification algorithm is proven through a simulation example.
基金This work was partially supported by the National Natural Science Foundation of China(No.60504008).
文摘The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional approach combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system; next, the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are developed. The results are given in terms of linear matrix inequalities (LMIs), which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme.
文摘The separation of the Lyapunov matrices and system matrices plays an important role when one uses parameter-dependent Lyapunov functional handling systems with polytopic type uncertainties. The delay-dependent robust stability problem for systems with polytopic type uncertainties is discussed by using parameter-dependent Lyapunov functional. The derivative term in the derivative of Lyapunov functional is reserved and the free weighting matrices are employed to express the relationship between die terms in the system equation such that the Lyapunov matrices are not involved in any product terms with the system matrices. In addition, the relationships between the terms in the Leibniz Newton formula are also described by some free weighting matrices and some delay-dependent stability conditions are derived. Numerical examples demonstrate that the proposed criteria are more effective than the previous results.
基金Project supported by the Fundamental Research Funds for the Central Universities of Ministry of Education of China(Grant No.2014JBM150)
文摘In this paper, the robust output feedback cruise control for high-speed train movement with uncertain parameters is investigated. The dynamic of a high-speed train is modeled by a cascade of cars connected by flexible couplers, which is subject to rolling mechanical resistance, aerodynamic drag and wind gust. Based on Lyapunov's stability theory, the sufficient condition for the existence of the robust output feedback cruise control law is given in terms of linear matrix inequalities(LMIs), under which the high-speed train tracks the desired speed, the relative spring displacement between the two neighboring cars is stable at the equilibrium state, and meanwhile a small prescribed H∞ disturbance attenuation level is guaranteed. One numerical example is given to illustrate the effectiveness of the proposed methods.
基金Project supported by the National Natural Science Foundation of China (Grant No.60674026)the Jiangsu Provincial Natural Science Foundation of China (Grant No.BK2007016)
文摘In this paper, we have improved delay-dependent stability criteria for recurrent neural networks with a delay varying over a range and Markovian jumping parameters. The criteria improve over some previous ones in that they have fewer matrix variables yet less conservatism. In addition, a numerical example is provided to illustrate the applicability of the result using the linear matrix inequality toolbox in MATLAB.
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The robust guaranteed cost filtering problem for a dass of linear uncertain stochastic systems with time delays is investigated. The system under study involves time delays, jumping parameters and Brownian motions. The transition of the jumping parameters in systems is governed by a finite-state Markov process. The objective is to design linear memoryless filters such that for all uncertainties, the resulting augmented system is robust stochastically stable independent of delays and satisfies the proposed guaranteed cost performance. Based on stability theory in stochastic differential equations, a sufficient condition on the existence of robust guaranteed cost filters is derived. Robust guaranteed cost filters are designed in terms of linear matrix inequalities. A convex optimization problem with LMI constraints is formulated to design the suboptimal guaranteed cost filters.
基金supported by the Australian Research Council(No.ARC LP0560077)and the University of Technology,Sydney,Australia
文摘This paper presents an approach in designing a robust controller for vehicle suspensions considering changes in vehicle inertial properties. A four-degree-of-freedom half-car model with active suspension is studied in this paper, and three main performance requirements are considered. Among these requirements, the ride comfort performance is optimized by minimizing the Ho~ norm of the transfer function from the road disturbance to the sprung mass acceleration, while the road holding performance and the suspension deflection limitation are guaranteed by constraining the generalized H2 (GH2) norms of the transfer functions from the road disturbance to the dynamic tyre load and the suspension deflection to be less than their hard limits, respectively. At the same time, the controller saturation problem is considered by constraining its peak response output to be less than a given limit using the GH2 norm as well. By solving the finite number of linear matrix inequalities (LMIs) with the minimization optimization procedure, the controller gains, which are dependent on the time-varying inertial parameters, can be obtained. Numerical simulations on both frequency and bump responses show that the designed parameter-dependent controller can achieve better active suspension performance compared with the passive suspension in spite of the variations of inertial parameters.
文摘The problem of robust L 1 filtering with pole constraint in a disk for linear continuous polytopic uncertain systems is discussed. The attention is focused on design a linear asymptotically stable filter such that the filtering error system remains robustly stable, and has a L 1 performance constraint and pole constraint in a disk. The new robust L 1 performance criteria and regional pole placement condition are obtained via parameter-dependent Lyapunov functions method. Upon the proposed multiobjective performance criteria and by means of LMI technique, both full-order and reduced-order robust L 1 filter with suitable dynamic behavior can be obtained from the solution of convex optimization problems. Compared with earlier result in the quadratic framework, this approach turns out to be less conservative. The efficiency of the proposed technique is demonstrated by a numerical example.
基金This work was supported in part by the Doctor Subject Foundation of China (No. 20050533015)the National Science Foundation of China(No. 60425310,60574014).
文摘This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties. A new and simple method is presented to directly decouple the Lyapunov matrix and the system dynamic matrix. Combining this method with the parameter-dependent Lyapunov function approach yields new criteria that include some existing ones as special cases. A numerical example illustrates the improvement over the existing ones.
基金supported by the National Natural Science Foundation of China (Nos. 60404001 and60774089)
文摘Feedback control problems for linear periodic systems (LPSs) with interval- type parameter uncertainties are studied in the discrete-time domain. First, the stability analysis and stabilization problems are addressed. Conditions based on the linear matrices inequality (LMI) for the asymptotical stability and state feedback stabilization, respec-tively, are given. Problems of L2-gain analysis and control synthesis are studied. For the L2-gain analysis problem, we obtain an LMI-based condition such that the autonomous uncertain LPS is asymptotically stable and has an L2-gain smaller than a positive scalar γ. For the control synthesis problem, we derive an LMI-based condition to build a state feedback controller ensuring that the closed-loop system is asymptotically stable and has an L2-gain smaller than the positive scalar γ. All the conditions are necessary and sufficient.
文摘The stability and stabilization of a class of nonlinear discrete time delayed systems(NDTDS) with time-varying delay and norm-bounded nonlinearity are investigated. Based on discrete time Lyapunov–Krasovskii functional method, a sufficient delaydependent condition for asymptotic stability of nonlinear systems is offered. Then, this condition is used to design a new efficient delayed state feedback controller(DSFC) for stabilization of such systems. These conditions are in the linear matrix inequality(LMI) framework. Illustrative examples confirm the improvement of the proposed approach over the similar cases. Furthermore, the obtained stability and stabilization conditions will be extended to uncertain discrete time delayed systems(UDTDS) with polytopic parameter uncertainties and also with norm-bounded parameter uncertainties.
基金Sponsored by the Scientific Research Foundation of Harbin Institute of Technology (Grant No.HIT.2003.02)the Chinese Outstanding Youth Science Foundation(Grant No. 69504002)
文摘This paper deals with the robust guaranteed cost observer with guaranteed cost performance for a class of linear uncertain jump systems with state delay.The transition of the jumping parameters in systems is governed by a finite-state Markov process.Based on the stability theory in stochastic differential equations,a sufficient condition on the existence of the proposed robust guaranteed cost observer is derived.Robust guaranteed cost observers are designed in terms of a set of linear coupled matrix inequalities.A convex optimization problem with LMI constraints is formulated to design the suboptimal guaranteed cost observers.
文摘This paper proposes new sufficient conditions for the exponential stability and stabilization.of linear uncertain polytopic time-delay systems. The conditions for exponential stability are expressed in terms of Kharitonov-type linear matrix inequalities (LMIs) and we develop control design methods based on LMIs for solving stabilization problem. Our method consists of a combination of the LMI approach and the use of parameter-dependent Lyapunov functionals, which allows to compute simultaneously the two bounds that characterize the exponetial stability rate of the solution. Numerical examples illustrating the conditions are given.