Stability Criteria of LPD System with Time-Varying Delay (original) (raw)
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Journal of the Franklin Institute, 2011
Convex conditions, expressed as linear matrix inequalities (LMIs), for stability analysis and robust design of uncertain discrete-time systems with time-varying delay are presented in this paper. Delaydependent and delay-independent convex conditions are given. This paper is particularly devoted to the synthesis case where convex conditions are proposed to consider maximum allowed delay interval. It is also presented some relaxed LMIs that yield less conservative conditions at the expense of increasing the computational burden. Extensions to cope with decentralized control and output feedback control are discussed. Numerical examples, including real world motivated models, are presented to illustrate the effectiveness of the proposed approach. (V.J.S. Leite). constant delay. The problem of robust filtering for discrete-time uncertain systems with delayed states is considered in some papers. Delayed state systems with norm-bounded uncertainties are studied in and with polytopic uncertainties in . In the last case the delay is time-invariant. Recently, the problem of output feedback has attracted attention and can be cited as examples of on going research. In special, presents results for precisely known systems with time-varying delay including both static output feedback (SOF) and dynamic output feedback. The conditions, however, are presented as an interactive method that relax some matrix inequalities. In time-varying delay is assumed and a nonlinear algorithm is proposed to obtain a stabilizing controller. In [24] the results of [11] are extended, including polytopic uncertainties and constant Lyapunov-Krasovskii matrices. An interesting application can be found in the context of network control system: although most of the studies in the literature on this subject deal with continuous-time models, nowadays there are some approaches using discrete-time models with delayed states . See also for a robust adaptive sliding mode control scheme applied to discrete-time systems with time-varying delay in the state and subject to norm-bounded uncertainties. In the context of discrete-time-varying systems with time-varying delay in the state, see for convex approaches to the dynamic output feedback controller design problem.
Robust stabilization of polytopic discrete-time systems with time-varying delay in the states
49th IEEE Conference on Decision and Control (CDC), 2010
Convex conditions, expressed as linear matrix inequalities (LMIs), for stability analysis and robust design of uncertain discrete-time systems with time-varying delay are presented in this paper. Delaydependent and delay-independent convex conditions are given. This paper is particularly devoted to the synthesis case where convex conditions are proposed to consider maximum allowed delay interval. It is also presented some relaxed LMIs that yield less conservative conditions at the expense of increasing the computational burden. Extensions to cope with decentralized control and output feedback control are discussed. Numerical examples, including real world motivated models, are presented to illustrate the effectiveness of the proposed approach. (V.J.S. Leite). constant delay. The problem of robust filtering for discrete-time uncertain systems with delayed states is considered in some papers. Delayed state systems with norm-bounded uncertainties are studied in and with polytopic uncertainties in . In the last case the delay is time-invariant. Recently, the problem of output feedback has attracted attention and can be cited as examples of on going research. In special, presents results for precisely known systems with time-varying delay including both static output feedback (SOF) and dynamic output feedback. The conditions, however, are presented as an interactive method that relax some matrix inequalities. In time-varying delay is assumed and a nonlinear algorithm is proposed to obtain a stabilizing controller. In [24] the results of [11] are extended, including polytopic uncertainties and constant Lyapunov-Krasovskii matrices. An interesting application can be found in the context of network control system: although most of the studies in the literature on this subject deal with continuous-time models, nowadays there are some approaches using discrete-time models with delayed states . See also for a robust adaptive sliding mode control scheme applied to discrete-time systems with time-varying delay in the state and subject to norm-bounded uncertainties. In the context of discrete-time-varying systems with time-varying delay in the state, see for convex approaches to the dynamic output feedback controller design problem.
Advances in Difference Equations, 2012
This article addresses the robust stability for a class of nonlinear uncertain discrete-time systems with convex polytopic of uncertainties. The system to be considered is subject to both interval time-varying delays and convex polytopic-type uncertainties. Based on the augmented parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent conditions for the robust stability are established in terms of linear matrix inequalities. An application to robust stabilization of nonlinear uncertain discrete-time control systems is given. Numerical examples are included to illustrate the effectiveness of our results. MSC: 15A09; 52A10; 74M05; 93D05
Journal of Applied Mathematics, 2013
This paper addresses the robust stability for a class of linear discrete-time stochastic systems with convex polytopic uncertainties. The system to be considered is subject to both interval time-varying delays and convex polytopic type uncertainties. Based on the augmented parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent conditions for the robust stability are established in terms of linear matrix inequalities. An application to robust stabilization of linear discrete-time stochastic control systems is given. Numerical examples are included to illustrate the effectiveness of our results.
Delay-dependent robust stability for stochastic time-delay systems with polytopic uncertainties
International Journal of Robust and Nonlinear Control, 2008
This paper considers a delay-dependent and parameter-dependent robust stability criterion for stochastic time-delay systems with polytopic uncertainties. The delay-dependent robust stability criterion, as expressed in terms of linear matrix inequalities (LMIs), is obtained by using parameter-dependent Lyapunov functions. It is shown that the result derived by a parameter-dependent Lyapunov functional is less conservative. Numerical examples are provided to illustrate the effectiveness of the proposed method.
Robust Stabilization of Discrete-Time Systems with Time-Varying Delay: An LMI Approach
Mathematical Problems in Engineering, 2008
Sufficient linear matrix inequality LMI conditions to verify the robust stability and to design robust state feedback gains for the class of linear discrete-time systems with time-varying delay and polytopic uncertainties are presented. The conditions are obtained through parameter-dependent Lyapunov-Krasovskii functionals and use some extra variables, which yield less conservative LMI conditions. Both problems, robust stability analysis and robust synthesis, are formulated as convex problems where all system matrices can be affected by uncertainty. Some numerical examples are presented to illustrate the advantages of the proposed LMI conditions.
IEEE Transactions on Automatic Control, 2004
This paper concerns the problem of the robust stability of a linear system with a time-varying delay and polytopictype uncertainties. In order to construct a parameter-dependent Lyapunov functional for the system, we first devised a new method of dealing with a time-delay system without uncertainties. In this method, the derivative terms of the state, which is in the derivative of the Lyapunov functional, are retained and some free weighting matrices are used to express the relationships among the system variables, and among the terms in the Leibniz-Newton formula. As a result, the Lyapunov matrices are not involved in any product terms of the system matrices in the derivative of the Lyapunov functional. This method is then easily extended to a system with polytopic-type uncertainties. Numerical examples demonstrate the validity of the proposed criteria.
New stability criteria for linear systems with interval time-varying delay
Automatica, 2008
This paper investigates robust stability of uncertain linear systems with interval time-varying delay. The time-varying delay is assumed to belong to an interval and is a fast time-varying function. The uncertainty under consideration includes polytopic-type uncertainty and linear fractional norm-bounded uncertainty. A new Lyapunov-Krasovskii functional, which makes use of the information of both the lower and upper bounds of the interval time-varying delay, is proposed to drive some new delay-dependent stability criteria. In order to obtain much less conservative results, a tighter bounding for some term is estimated. Moreover, no redundant matrix variable is introduced. Finally, three numerical examples are given to show the effectiveness of the proposed stability criteria.
Exponential stability of linear uncertain polytopic systems with distributed time-varying delays
math.spbu.ru
In this paper, a class of uncertain linear polytopic systems with distributed time varying delays is studied. By using an improved parameter dependent Lyapunov-Krasovskii functional approach and linear matrix inequality technique, delay-dependent sufficient conditions for exponential stability of the system are first established in terms of Mondie-Kharitonov type's linear matrix inequalities (LMIs). Numerical example is presented to demonstrate the effectiveness of the proposed conditions.
A convex approach for robust state feedback control of discrete-time systems with state delay
2004
In this paper, uncertain discrete-time systems with state delay are investigated. The uncertainty is supposed to belong to a known convex polytope. Linear matrix inequality conditions are given for the robust stability of the system, encompassing quadratic stability based results. Then, convex conditions assuring the existence of a robust state feedback gain are derived, assuring the delay independent quadratic stability of the closed-loop system (thus allowing to deal with time-varying uncertain systems) or, in the time-invariant case, guaranteeing the robust stability irrespective of the value of the delay. Moreover, the feedback control law can also include a term depending on the delayed state which, if the value of the delay is known, can be used to improve the control design. Numerical examples illustrate the effectiveness of the proposed techniques.