H∞ Guaranteed Cost Filtering for Uncertain Discrete-Time Switched Systems With Multiple Time-Varying Delays

This paper deals with the problem of H ∞ guaranteed cost filtering for uncertain discrete-time switched systems with multiple time-varying delays. The switched system under consideration is subject to time-varying norm-bounded parameter uncertainties in all the system matrices. The aim is to design a filter, which guarantees the asymptotical stability of the error system with prescribed disturbance attenuation for all admissible uncertainties and the cost function value is not more than a specified upper bound. By resorting to a switched Lyapunov function, some delay-dependent sufficient conditions are presented in terms of linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of the proposed algorithms.

[1]  Linlin Hou,et al.  Robust l2−l∞ state feedback control for uncertain discrete-time switched systems with mode-dependent time-varying delays† , 2010 .

[2]  Qing-Long Han,et al.  Robust Hinfinity filtering for a class of uncertain linear systems with time-varying delay , 2008, Autom..

[3]  Le Yi Wang,et al.  Identification of cascaded systems with linear and quantized observations , 2009 .

[4]  Huijun Gao,et al.  New Results on Stability of Discrete-Time Systems With Time-Varying State Delay , 2007, IEEE Transactions on Automatic Control.

[5]  Shengyuan Xu,et al.  A survey of linear matrix inequality techniques in stability analysis of delay systems , 2008, Int. J. Syst. Sci..

[6]  Pedro Luis Dias Peres,et al.  Robust 𝒽∞ filtering for uncertain discrete-time state-delayed systems , 2001, IEEE Trans. Signal Process..

[7]  Emilia Fridman,et al.  A new H∞ filter design for linear time delay systems , 2001, IEEE Trans. Signal Process..

[8]  Shengyuan Xu,et al.  Improved stability criterion and its applications in delayed controller design for discrete-time systems , 2008, Autom..

[9]  Young Soo Moon,et al.  Delay-dependent robust stabilization of uncertain state-delayed systems , 2001 .

[10]  M. Branicky Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[11]  A. Morse,et al.  Basic problems in stability and design of switched systems , 1999 .

[12]  Wei Wang,et al.  Stability Analysis for Linear Switched Systems With Time-Varying Delay , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[13]  Jamal Daafouz,et al.  Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach , 2002, IEEE Trans. Autom. Control..

[14]  Emilia Fridman,et al.  Delay-Dependent H∞ Control of Uncertain Discrete Delay Systems , 2005, Eur. J. Control.

[15]  Shengyuan Xu,et al.  Robust H∞ stabilization for uncertain switched impulsive control systems with state delay: An LMI approach , 2008 .

[16]  Shengyuan Xu,et al.  Improved delay-dependent stability criteria for time-delay systems , 2005, IEEE Transactions on Automatic Control.

[17]  Peng Shi,et al.  $H_\infty$ Filtering of Discrete-Time Switched Systems With State Delays via Switched Lyapunov Function Approach , 2007, IEEE Transactions on Automatic Control.

[18]  Huijun Gao,et al.  Robust H∞ filtering for switched linear discrete‐time systems with polytopic uncertainties , 2006 .

[19]  Qing-Long Han,et al.  Delay-Dependent Robust $H_{\infty}$ Filtering for Uncertain Discrete-Time Systems With Time-Varying Delay Based on a Finite Sum Inequality , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[20]  Jong Hae Kim,et al.  Guaranteed cost and H∞ filtering for discrete-time polytopic uncertain systems with time delay , 2005, J. Frankl. Inst..

[21]  Shengyuan Xu,et al.  Simplified descriptor system approach to delay-dependent stability and performance analyses for time-delay systems , 2005 .

[22]  M. Zaremba,et al.  Quadratic stability of a class of switched nonlinear systems , 2004, IEEE Transactions on Automatic Control.

[23]  A. Morse,et al.  Stability of switched systems with average dwell-time , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).