IMPROVED DELAY-DEPENDENT ROBUST EXPONENTIAL STABILIZATION CRITERIA FOR UNCERTAIN TIME-VARYING DELAY SINGULAR SYSTEMS

This paper is concerned with the stability and stabilization for singular systems with time-varying delay. Firstly, by defining a novel Lyapunov function, a delaydependent stability criterion, which ensures that the nominal unforced singular timevarying delay system is regular, impulse free and asymptotically stable, is established in terms of integral inequality approach (IIA) and linear matrix inequalities (LMIs). Then based on the obtained criteria, the exponential robust stability and stabilization problems are solved and the explicit expressions of the desired state feedback control laws are also given. Numerical examples are given to demonstrate the effectiveness and the benefits of the obtained results.

[1]  W. Gui,et al.  A less conservative delay-dependent stability for uncertain singular linear systems with time-delays , 2010, 2010 8th World Congress on Intelligent Control and Automation.

[2]  James Lam,et al.  Delay-dependent robust exponential stability of uncertain descriptor systems with time-varying delays , 2005 .

[3]  F. Lewis.  A survey of linear singular systems , 1986 .

[4]  Zhaolin Cheng,et al.  Delay-dependent State Feedback Guaranteed Cost Control for Uncertain Singular Time-delay Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[5]  Yeong-Jeu Sun.  Exponential stability for continuous-time singular systems with multiple time delays , 2003 .

[6]  Pin-Lin Liu,et al.  Exponential stability for linear time-delay systems with delay dependence , 2003, J. Frankl. Inst..

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

[8]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[9]  Shen Yanxia,et al.  Delay-dependent Robust Stabilization for a Class of Uncertain Switched Singular Systems with Time-delay , 2012 .

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

[11]  Zheng-Guang Wu,et al.  Robust Exponential Stability of Uncertain Singular Markovian Jump Time-delay Systems , 2010 .

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

[13]  Pin-Lin Liu,et al.  Robust exponential stability for uncertain time-varying delay systems with delay dependence , 2009, J. Frankl. Inst..

[14]  E. Boukas,et al.  DELAY-DEPENDENT STABILIZATION OF SINGULAR LINEAR SYSTEMS WITH DELAYS , 2006 .

[15]  El-Kebir Boukas,et al.  Deterministic and Stochastic Time-Delay Systems , 2002 .

[16]  Q.-L. Han,et al.  Delay-dependent robust H∞ controller design for uncertain descriptor systems with time-varying discrete and distributed delays , 2005 .

[17]  E. Boukas,et al.  Delay-Dependent Stability Analysis of Singular Linear Continuous-time System , 2003, 2003 4th International Conference on Control and Automation Proceedings.