Delay-dependent stability and H∞ control for uncertain discrete switched singular systems with time-delay

Abstract The robust stability, robust stabilization and H ∞ control problems for time-delay discrete switched singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent (r.s.e.) transformation and by introducing new state vectors, the switched singular system is transformed into a switched standard linear system, and delay-dependent linear matrix inequality (LMI) conditions for the time-delay discrete-time switched singular systems to be regular, causal and uniformly asymptotically stable; uniformly robust asymptotically stable with γ-disturbance attenuation are obtained, respectively. With these conditions, robust stabilization problem and robust H ∞ control problem are solved based on LMIs.

[1]  Emilia Fridman,et al.  An improved stabilization method for linear time-delay systems , 2002, IEEE Trans. Autom. Control..

[2]  Yuan Gong Sun,et al.  Delay-dependent robust stability and stabilization for discrete-time switched systems with mode-dependent time-varying delays , 2006, Appl. Math. Comput..

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

[4]  Zhaolin Cheng,et al.  An LMI approach to robust stabilization for uncertain discrete-time singular systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[5]  Shaosheng Zhou,et al.  Generalized H2 output feedback controller design for uncertain discrete-time switched systems via switched Lyapunov functions , 2006 .

[6]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[7]  I. Petersen.  A stabilization algorithm for a class of uncertain linear systems , 1987 .

[8]  Lihua Xie,et al.  Robust H/sub infinity / control for linear systems with norm-bounded time-varying uncertainty , 1992 .

[9]  Shengyuan Xu,et al.  Robust stability and stabilization of discrete singular systems: an equivalent characterization , 2004, IEEE Transactions on Automatic Control.

[10]  Guangming Xie,et al.  Delay-dependent robust stability and Hinfinity control for uncertain discrete-time switched systems with mode-dependent time delays , 2007, Appl. Math. Comput..

[11]  Zhaolin Cheng,et al.  Delay-Dependent Robust Stability Criteria for Two Classes of Uncertain Singular Time-Delay Systems , 2007, IEEE Transactions on Automatic Control.

[12]  Vu Ngoc Phat,et al.  Robust stability and stabilizability of uncertain linear hybrid systems with state delays , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[13]  Shengyuan Xu,et al.  Robust stability and stabilization for singular systems with state delay and parameter uncertainty , 2002, IEEE Trans. Autom. Control..

[14]  Zhang You-gang.  Delay-dependent robust stability criteria for two classes of uncertain singular time-delay systems , 2008 .

[15]  P. Shi.  On H∞ Control Design for Singular Continuous-Time Delay Systems with Parametric Uncertainties , 2004 .

[16]  S Xu,et al.  Robust H∞ Control for Discrete Singular Systems with State Delay and Parameter Uncertainty , 2002 .

[17]  Zhang,et al.  Output Feedback Based Admissible Control of Switched Linear Singular Systems , 2006 .

[18]  Bin Meng,et al.  Reachability conditions for switched linear singular systems , 2006, IEEE Transactions on Automatic Control.

[19]  Xinzhi Liu,et al.  Stability of a class of linear switching systems with time delay , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[20]  Carmen Coll,et al.  Positive N-periodic descriptor control systems , 2004, Syst. Control. Lett..

[21]  Gang Yin,et al.  Hybrid singular systems of differential equations , 2002, Science in China Series F: Information Sciences.

[22]  Ji-Woong Lee,et al.  Uniform stabilization of discrete-time switched and Markovian jump linear systems , 2006, Autom..

[23]  Long Wang,et al.  LMI approach to L/sub 2/-gain analysis and control synthesis of uncertain switched systems , 2004 .

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

[25]  S. Ma,et al.  Delay-dependent robust H∞ control for uncertain discrete-time singular systems with time-delays , 2008 .

[26]  P. Shi.  On H∞ Control Design for Singular Continuous-Time Delay Systems with Parametric Uncertainties , 2004 .

[27]  Emilia Fridman,et al.  A descriptor system approach to H∞ control of linear time-delay systems , 2002, IEEE Trans. Autom. Control..

[28]  L. Xie,et al.  Robust H^∞ Control for Linear Systems with Norm-Bounded Time-Varying Uncertainty , 1990 .