Delay-dependent robust stability and stabilisation for uncertain discrete singular systems with time-varying delays

The robust stability and robust stabilisation problems for time-varying delay discrete singular systems with parameter uncertainties are discussed. A delay-dependent linear matrix inequality (LMI) condition to enable time-varying delay discrete standard state-space systems to be stable is given. Based on this condition and the restricted system equivalent transformation, the delay-dependent LMI condition is proposed for the time-varying delay discrete singular systems to be admissible. With this condition, the problems of robust stability and robust stabilisation are solved, and the delay-dependent LMI conditions are obtained. Numerical examples illustrate the effectiveness of the proposed method.

[1]  D. Luenberger.  Dynamic equations in descriptor form , 1977 .

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

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

[4]  J. Aplevich.  Implicit Linear Systems , 1991 .

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

[6]  Seong-Ho Song,et al.  H∞ Control of discrete-time linear systems with norm-bounded uncertainties and time delay in state , 1998, Autom..

[7]  Shengyuan Xu,et al.  Stabilization of discrete-time singular systems: a matrix inequalities approach , 1999, Autom..

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

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

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

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

[12]  J. Lam,et al.  Reliable H control of uncertain descriptor systems with multiple time delays , 2003 .

[13]  E. Fridman,et al.  Delay-dependent stability and H ∞ control: Constant and time-varying delays , 2003 .

[14]  Wu-Hua Chen,et al.  Delay-dependent stability and H∞ control of uncertain discrete-time Markovian jump systems with mode-dependent time delays , 2004, Syst. Control. Lett..

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

[16]  Wook Hyun Kwon,et al.  Delay-dependent robust Hinfinity control for uncertain systems with a state-delay , 2004, Autom..

[17]  Jin-Hua She,et al.  New delay-dependent stability criteria and stabilizing method for neutral systems , 2004, IEEE Trans. Autom. Control..

[18]  Shin-Ju Chen,et al.  Robust stability of discrete time-delay uncertain singular systems , 2004 .

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