New delay‐dependent robust stability of discrete singular systems with time‐varying delay

The robust stability of discrete singular systems with time‐varying delay is considered. New delay‐dependent stability criteria are proposed, which are dependent on the minimum and maximum delay bounds. A strict delay‐dependent linear matrix inequality (LMI) condition is obtained for a discrete singular time‐varying system to be regular, causal and stable. The result on robust stabilization of uncertain discrete singular time‐varying systems is also obtained and expressed in terms of LMIs. Numerical examples are given to demonstrate the applicability of the proposed method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

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

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

[3]  Xi Li,et al.  Criteria for robust stability and stabilization of uncertain linear systems with state delay , 1997, Autom..

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

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

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

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

[8]  Shinn-Horng Chen,et al.  D-stability robustness for linear discrete uncertain singular systems with delayed perturbations , 2004 .

[9]  Huijun Gao,et al.  Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay , 2004 .

[10]  Zhaolin Cheng,et al.  Delay-dependent Robust Resilient H ∞ Control for Uncertain Singular Time-delay Systems , 2005 .

[11]  Ralph R. Martin,et al.  Delay-dependent robust stabilisation of discrete-time systems with time-varying delay , 2006 .

[12]  Renxin Zhong,et al.  DELAY‐DEPENDENT ROBUST CONTROL OF DESCRIPTOR SYSTEMS WITH TIME DELAY , 2006 .

[13]  R. Lu,et al.  Delay-Dependent Robust Stability of Uncertain Discrete Singular Time-Delay Systems , 2006, 2006 6th World Congress on Intelligent Control and Automation.

[14]  Chen Yun,et al.  Delay-dependent robust H∞ control for uncertain discrete singular time-varying delay systems based on a finite sum inequality , 2006, 2007 Chinese Control Conference.

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

[16]  S. Ma,et al.  Delay-dependent robust stability and stabilisation for uncertain discrete singular systems with time-varying delays , 2007 .

[17]  Wuneng Zhou,et al.  Delay-dependent Robust Stabilization for Uncertain Singular Systems with State Delay , 2007 .

[18]  Z. Wu,et al.  Delay-dependent robust H/sub /spl infin// control for uncertain singular time-delay systems , 2007 .

[19]  Huaicheng Yan,et al.  New delay-dependent stability criteria of uncertain linear systems with multiple time-varying state delays , 2008 .