The problem of delay-dependent criteria for the robust stability of neutral systems with time-varying structured uncertainties and identi-cal neutral-delay and discrete-delay is concerned. A criterion for nominal syst...The problem of delay-dependent criteria for the robust stability of neutral systems with time-varying structured uncertainties and identi-cal neutral-delay and discrete-delay is concerned. A criterion for nominal systems is presented by taking the relationship between the terms in the Leibniz-Newton formula into account, which is described by some free-weighting matrices. In addition, this criterion is extended to robust stability of the systems with time-varying structured uncertainties. All of the criteria are based on linear matrix inequality such that it is easy to calculate the upper bound of the time-delay and the free-weighting matrices. Numerical examples illustrate the effectiveness and the improvement over the existing results.展开更多
The stability and stabilization of a class of linear switched time-varying delay systems are investigated. A piecewise quadratic Lyapunov function （PWQLF） is constructed and is used to obtain the stability condition...The stability and stabilization of a class of linear switched time-varying delay systems are investigated. A piecewise quadratic Lyapunov function （PWQLF） is constructed and is used to obtain the stability conditions based on the linear matrix inequalities （LMIs）. The stabilizing controller for this class of system is then designed and the solution of the desired controller can be obtained by a cone complementary linearization algorithm. Numerical examples are provided to illustrate the less conservativeness of the new stability and the validity of the controller design procedures.展开更多
This article considers delay dependent decentralized H∞ filtering for a class of uncertain interconnected systems, where the uncertainties are assumed to be time varying and satisfy the norm-bounded conditions. First...This article considers delay dependent decentralized H∞ filtering for a class of uncertain interconnected systems, where the uncertainties are assumed to be time varying and satisfy the norm-bounded conditions. First, combining the Lyapunov-Krasovskii functional approach and the delay integral inequality of matrices, a sufficient condition of the existence of the robust decentralized H∞ filter is derived, which makes the error systems asymptotically stable and satisfies the H∞ norm of the transfer function from noise input to error output less than the specified up-bound on the basis of the form of uncertainties. Then, the above sufficient condition is transformed to a system of easily solvable LMIs via a series of equivalent transformation. Finally, the numerical simulation shows the efficiency of the main results.展开更多
The robust passivity control problem is addressed for a class of uncertain delayed systems with timevarying delay. The parameter uncertainties are norm-bounded. First, the delay-dependent stability sufficient conditio...The robust passivity control problem is addressed for a class of uncertain delayed systems with timevarying delay. The parameter uncertainties are norm-bounded. First, the delay-dependent stability sufficient condition is obtained for the nominal system, and then, based-on the former, the delay-dependent robust passivity criteria is provided and the corresponding controller is designed in terms of linear matrix inequalities. Finally, a numerical example is given to demonstrate the validity of the proposed approach.展开更多
This paper deals with the problem of stability for systems with delay varying in an interval.A new Lyapunov functional,which makes use of the information of both the lower and upper bounds of the interval time-varying...This paper deals with the problem of stability for systems with delay varying in an interval.A new Lyapunov functional,which makes use of the information of both the lower and upper bounds of the interval time-varying delay,is proposed to derive some new stability criteria.Furthermore,the relationship of the time-varying delay and its lower bound and upper bound is taken into account.As a result,some less conservative delay-dependent stability criteria are obtained without ignoring any useful information in the derivative of Lyapunov functional,which are established in the forms of linear matrix inequalities.Numerical examples are provided to show that the obtained results are better than existing ones.展开更多
The robust H∞ control problem for a class of uncertain Takagi-Sugeno fuzzy systems with timevarying state delays is studied. The uncertain parameters are supposed to reside in a polytope. Based on the delay-dependent...The robust H∞ control problem for a class of uncertain Takagi-Sugeno fuzzy systems with timevarying state delays is studied. The uncertain parameters are supposed to reside in a polytope. Based on the delay-dependent Lyapunov functional method, a new delay-dependent robust H∞ fuzzy controller, which depends on the size of the delays and the derivative of the delays, is presented in term of linear matrix inequalities （LMIs）. For all admissible uncertainties and delays, the controller guarantees not only the asymptotic stability of the system but also the prescribed H∞ attenuation level. In addition, the effectiveness of the proposed design method is demonstrated by a numerical example.展开更多
The problem of designing a non-fragile delay-dependent H∞ state-feedback controller was investigated for a linear time-delay system with uncertainties in state and control input. First, a recently derived integral in...The problem of designing a non-fragile delay-dependent H∞ state-feedback controller was investigated for a linear time-delay system with uncertainties in state and control input. First, a recently derived integral inequality method and Lyapunov-Krasovskii stability theory were used to derive new delay-dependent bounded real lemmas for a non-fragile state-feedback controller containing additive or multiplicative uncertainties. They ensure that the closed-loop system is internally stable and has a given H∞ disturbance attenuation level. Then, methods of designing a non-fragile H∞ state feedback controller were presented. No parameters need to be tuned and can be easily determined by solving linear matrix inequalities. Finally, the validity of the proposed methods was demonstrated by a numerical example with the asymptotically stable curves of system state and controller output under the initial condition of x(0)=1 0 -1]T and h=0.8 time-delay boundary.展开更多
The problem of delay-dependent passive control of a class of linear systems with nonlinear perturbation and time-varying delay in states is studied. The main idea aims at designing a state-feedback controller such tha...The problem of delay-dependent passive control of a class of linear systems with nonlinear perturbation and time-varying delay in states is studied. The main idea aims at designing a state-feedback controller such that for a time-varying delay in states, the linear system with nonlinear perturbation remains robustly stable and passive. In the system, the delay is time-varying. And the derivation of delay has the maximum and minimum value. The time-varying nonlinear perturbation is allowed to be norm-bounded. Using the effective linear matrix inequality methodology, the sufficient condition is primarily obtained for the system to have robust stability and passivity. Subsequently the existent condition of a state feedback controller is given, and the explicit expression of the controller is obtained by means of the solution of linear matrix inequalities （LMIs）. In the end, a numerical example is given to demonstrate the validity and applicability of the proposed approach.展开更多
The robust H∞ control problem of norm bounded uncertain discrete Takagi-Sugeno （T-S） fuzzy systems with state delay is addressed. First, by constructing an appropriate basis-dependent Lyapunov-Krasovskii function, ...The robust H∞ control problem of norm bounded uncertain discrete Takagi-Sugeno （T-S） fuzzy systems with state delay is addressed. First, by constructing an appropriate basis-dependent Lyapunov-Krasovskii function, a new delay-dependent sufficient condition on robust H∞-disturbance attenuation is presented, in which both robust stability and prescribed H∞ performance are guaranteed to be achieved. Then based on the condition, a delay-dependent robust Hoo controller design scheme is developed in term of a convex algorithm. Finally, examples are given to illustrate the effectiveness of the proposed method.展开更多
The problem of robust stabilization for uncertain singular time-delay systems is studied. First, a new delay-dependent asymptotic stability criteria for normal singular time-delay systems is given, which is less conse...The problem of robust stabilization for uncertain singular time-delay systems is studied. First, a new delay-dependent asymptotic stability criteria for normal singular time-delay systems is given, which is less conservative. Using this result, the problem of state feedback robust stabilization for uncertain singular time-delay systems is discussed, Finally, two examples are given to illustrate the effectiveness of the results.展开更多
The problems of robust stability and stabilization via memoryless state feedback for a class of discrete-time switched singular systems with time-varying delays and linear fractional uncertainties are investigated.By ...The problems of robust stability and stabilization via memoryless state feedback for a class of discrete-time switched singular systems with time-varying delays and linear fractional uncertainties are investigated.By constructing a novel switched Lyapunov-Krasovskii functional,a delay-dependent criterion for the unforced system to be regular,causal and uniformly asymptotically stable is established in terms of linear matrix inequalities（LMIs）.An explicit expression for the desired memoryless state feedback stabilization controller is also given.The merits of the proposed criteria lie in their less conservativeness and relative simplicity,which are achieved by considering additionally useful terms（ignored in previous methods） when estimating the upper bound of the forward difference of the Lyapunov-Krasovskii functional and by avoiding utilizing any model augmentation transformation.Some numerical examples are provided to illustrate the validity of the proposed methods.展开更多
Delay-dependent robust stability of cellular neural networks with time-varying discrete and distributed time-varying delays is considered. Based on Lyapunov stability theory and the linear matrix inequality （LMIs） t...Delay-dependent robust stability of cellular neural networks with time-varying discrete and distributed time-varying delays is considered. Based on Lyapunov stability theory and the linear matrix inequality （LMIs） technique, delay-dependent stability criteria are derived in terms of LMIs avoiding bounding certain cross terms, which often leads to conservatism. The effectiveness of the proposed stability criteria and the improvement over the existing results are illustrated in the numerical examples.展开更多
A robust dissipative control problem for a class of It-type stochastic systems is discussed with Markovian jumping parameters and time-varying delay. A memoryless state feedback dissipative controller is developed bas...A robust dissipative control problem for a class of It-type stochastic systems is discussed with Markovian jumping parameters and time-varying delay. A memoryless state feedback dissipative controller is developed based on Lyapunov-Krasovskii functional approach such that the closed-loop system is robustly stochastically stable and weakly delay-dependent （RSSWDD） and strictly （Q, S, R）-dissipative. The sufficient condition on the existence of state feedback dissipative controller is presented by linear matrix inequality （LMI）. And the desired controller can be concluded as solving a set of LMI. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.展开更多
The problem of delay-dependent stability and guaranteed cost control （GCC） for a class of uncertain time-delay Lur＇e systems are studied. By using an improved integral inequality,a less conservative delay-dependent...The problem of delay-dependent stability and guaranteed cost control （GCC） for a class of uncertain time-delay Lur＇e systems are studied. By using an improved integral inequality,a less conservative delay-dependent stability criterion is formulated as the feasibility problem of the linear matrix inequality （LMI）. The criterion is proved theoretically to be less conservative than some existing results for linear time-delay systems. Because of the fact that the matrices in the LMI-based stability criteria usually have different dimensions, different structures, and different variables, the conservatism analysis of the criteria is difficult. This study brings about a new insight into the comparison of conservatism among different stability criteria, which are expressed in certain LMI forms. The existence of the guaranteed cost controller is given in terms of matrix inequalities. The condition can be solved by using an iterative procedure and does not need any parameter tuning. A numerical example is given to illustrate the effectiveness of the proposed method.展开更多
文摘The problem of delay-dependent criteria for the robust stability of neutral systems with time-varying structured uncertainties and identi-cal neutral-delay and discrete-delay is concerned. A criterion for nominal systems is presented by taking the relationship between the terms in the Leibniz-Newton formula into account, which is described by some free-weighting matrices. In addition, this criterion is extended to robust stability of the systems with time-varying structured uncertainties. All of the criteria are based on linear matrix inequality such that it is easy to calculate the upper bound of the time-delay and the free-weighting matrices. Numerical examples illustrate the effectiveness and the improvement over the existing results.
基金the National Natural Science Foundation of China (69874008).
文摘The stability and stabilization of a class of linear switched time-varying delay systems are investigated. A piecewise quadratic Lyapunov function （PWQLF） is constructed and is used to obtain the stability conditions based on the linear matrix inequalities （LMIs）. The stabilizing controller for this class of system is then designed and the solution of the desired controller can be obtained by a cone complementary linearization algorithm. Numerical examples are provided to illustrate the less conservativeness of the new stability and the validity of the controller design procedures.
基金the National Natural Science Foundation of China (60634020)the Hunan Provincial Natural Science Foundation of China (07JJ6138)+1 种基金the Postdoctoral Science Foundation of China (20060390883)the China Ph.D. Discipline Special Foundation (20050533028).
文摘This article considers delay dependent decentralized H∞ filtering for a class of uncertain interconnected systems, where the uncertainties are assumed to be time varying and satisfy the norm-bounded conditions. First, combining the Lyapunov-Krasovskii functional approach and the delay integral inequality of matrices, a sufficient condition of the existence of the robust decentralized H∞ filter is derived, which makes the error systems asymptotically stable and satisfies the H∞ norm of the transfer function from noise input to error output less than the specified up-bound on the basis of the form of uncertainties. Then, the above sufficient condition is transformed to a system of easily solvable LMIs via a series of equivalent transformation. Finally, the numerical simulation shows the efficiency of the main results.
文摘The robust passivity control problem is addressed for a class of uncertain delayed systems with timevarying delay. The parameter uncertainties are norm-bounded. First, the delay-dependent stability sufficient condition is obtained for the nominal system, and then, based-on the former, the delay-dependent robust passivity criteria is provided and the corresponding controller is designed in terms of linear matrix inequalities. Finally, a numerical example is given to demonstrate the validity of the proposed approach.
基金supported by the National Natural Science Foundation of China (60874025)the Natural Science Foundation of Hunan Province(10JJ6098)the Scientific Research Fund of Hunan Provincial Education Department (10C0638)
文摘This paper deals with the problem of stability for systems with delay varying in an interval.A new Lyapunov functional,which makes use of the information of both the lower and upper bounds of the interval time-varying delay,is proposed to derive some new stability criteria.Furthermore,the relationship of the time-varying delay and its lower bound and upper bound is taken into account.As a result,some less conservative delay-dependent stability criteria are obtained without ignoring any useful information in the derivative of Lyapunov functional,which are established in the forms of linear matrix inequalities.Numerical examples are provided to show that the obtained results are better than existing ones.
文摘The robust H∞ control problem for a class of uncertain Takagi-Sugeno fuzzy systems with timevarying state delays is studied. The uncertain parameters are supposed to reside in a polytope. Based on the delay-dependent Lyapunov functional method, a new delay-dependent robust H∞ fuzzy controller, which depends on the size of the delays and the derivative of the delays, is presented in term of linear matrix inequalities （LMIs）. For all admissible uncertainties and delays, the controller guarantees not only the asymptotic stability of the system but also the prescribed H∞ attenuation level. In addition, the effectiveness of the proposed design method is demonstrated by a numerical example.
基金Project(60574014) supported by the National Natural Science Foundation of ChinaProject(20050533015) supported by the Doctor Subject Foundation of ChinaProject(60425310) supported by the National Science Foundation for Distinguished Youth Scholars, China
文摘The problem of designing a non-fragile delay-dependent H∞ state-feedback controller was investigated for a linear time-delay system with uncertainties in state and control input. First, a recently derived integral inequality method and Lyapunov-Krasovskii stability theory were used to derive new delay-dependent bounded real lemmas for a non-fragile state-feedback controller containing additive or multiplicative uncertainties. They ensure that the closed-loop system is internally stable and has a given H∞ disturbance attenuation level. Then, methods of designing a non-fragile H∞ state feedback controller were presented. No parameters need to be tuned and can be easily determined by solving linear matrix inequalities. Finally, the validity of the proposed methods was demonstrated by a numerical example with the asymptotically stable curves of system state and controller output under the initial condition of x(0)=1 0 -1]T and h=0.8 time-delay boundary.
基金the National Natural Science Foundation of China (60674026 60574051).
文摘The problem of delay-dependent passive control of a class of linear systems with nonlinear perturbation and time-varying delay in states is studied. The main idea aims at designing a state-feedback controller such that for a time-varying delay in states, the linear system with nonlinear perturbation remains robustly stable and passive. In the system, the delay is time-varying. And the derivation of delay has the maximum and minimum value. The time-varying nonlinear perturbation is allowed to be norm-bounded. Using the effective linear matrix inequality methodology, the sufficient condition is primarily obtained for the system to have robust stability and passivity. Subsequently the existent condition of a state feedback controller is given, and the explicit expression of the controller is obtained by means of the solution of linear matrix inequalities （LMIs）. In the end, a numerical example is given to demonstrate the validity and applicability of the proposed approach.
文摘The robust H∞ control problem of norm bounded uncertain discrete Takagi-Sugeno （T-S） fuzzy systems with state delay is addressed. First, by constructing an appropriate basis-dependent Lyapunov-Krasovskii function, a new delay-dependent sufficient condition on robust H∞-disturbance attenuation is presented, in which both robust stability and prescribed H∞ performance are guaranteed to be achieved. Then based on the condition, a delay-dependent robust Hoo controller design scheme is developed in term of a convex algorithm. Finally, examples are given to illustrate the effectiveness of the proposed method.
基金the National Natural Science Foundation of China (60474047)Key Project of Natural Science Foundation of Guangdong Province (06105413).
文摘The problem of robust stabilization for uncertain singular time-delay systems is studied. First, a new delay-dependent asymptotic stability criteria for normal singular time-delay systems is given, which is less conservative. Using this result, the problem of state feedback robust stabilization for uncertain singular time-delay systems is discussed, Finally, two examples are given to illustrate the effectiveness of the results.
基金supported by the National Natural Science Foundation of China(6090402060835001)the Jiangsu Planned Projects for Postdoctoral Research Funds(0802010C)
文摘The problems of robust stability and stabilization via memoryless state feedback for a class of discrete-time switched singular systems with time-varying delays and linear fractional uncertainties are investigated.By constructing a novel switched Lyapunov-Krasovskii functional,a delay-dependent criterion for the unforced system to be regular,causal and uniformly asymptotically stable is established in terms of linear matrix inequalities（LMIs）.An explicit expression for the desired memoryless state feedback stabilization controller is also given.The merits of the proposed criteria lie in their less conservativeness and relative simplicity,which are achieved by considering additionally useful terms（ignored in previous methods） when estimating the upper bound of the forward difference of the Lyapunov-Krasovskii functional and by avoiding utilizing any model augmentation transformation.Some numerical examples are provided to illustrate the validity of the proposed methods.
文摘Delay-dependent robust stability of cellular neural networks with time-varying discrete and distributed time-varying delays is considered. Based on Lyapunov stability theory and the linear matrix inequality （LMIs） technique, delay-dependent stability criteria are derived in terms of LMIs avoiding bounding certain cross terms, which often leads to conservatism. The effectiveness of the proposed stability criteria and the improvement over the existing results are illustrated in the numerical examples.
基金supported in part by the National Natural Science Foundation of China (60874045 60904030)+1 种基金the Foundation of the Education Bureau of Jiangsu Province (09KJB510019)the Natural Science Foundation of Jiangsu Province (BK2009184)
文摘A robust dissipative control problem for a class of It-type stochastic systems is discussed with Markovian jumping parameters and time-varying delay. A memoryless state feedback dissipative controller is developed based on Lyapunov-Krasovskii functional approach such that the closed-loop system is robustly stochastically stable and weakly delay-dependent （RSSWDD） and strictly （Q, S, R）-dissipative. The sufficient condition on the existence of state feedback dissipative controller is presented by linear matrix inequality （LMI）. And the desired controller can be concluded as solving a set of LMI. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.
基金the National Science Foundation for Distinguished Youth Scholars of China(60525304)the Natural Science Foundation of Zhejiang Province (Y107657).
文摘The problem of delay-dependent stability and guaranteed cost control （GCC） for a class of uncertain time-delay Lur＇e systems are studied. By using an improved integral inequality,a less conservative delay-dependent stability criterion is formulated as the feasibility problem of the linear matrix inequality （LMI）. The criterion is proved theoretically to be less conservative than some existing results for linear time-delay systems. Because of the fact that the matrices in the LMI-based stability criteria usually have different dimensions, different structures, and different variables, the conservatism analysis of the criteria is difficult. This study brings about a new insight into the comparison of conservatism among different stability criteria, which are expressed in certain LMI forms. The existence of the guaranteed cost controller is given in terms of matrix inequalities. The condition can be solved by using an iterative procedure and does not need any parameter tuning. A numerical example is given to illustrate the effectiveness of the proposed method.
