Further results on stability criteria for linear systems with time-varying delay

The issue of stability of linear systems with time-varying delay is considered in this paper. By constructing a new type of Lyapunov functional which contains a novel triple integral term and using Finsler's lemma, new delay-dependent stability criteria are derived in terms of linear matrix inequality (LMI). Numerical examples are given to illustrate the effectiveness of the proposed method.

[1]  Huijun Gao,et al.  Comments and further results on "A descriptor system approach to H∞ control of linear time-delay systems" , 2003, IEEE Trans. Autom. Control..

[2]  Zhou Luan-jie,et al.  Delay-Dependent Robust Stabilization of Uncertain State-Delayed Systems , 2004 .

[3]  Yong He,et al.  Delay-dependent criteria for robust stability of time-varying delay systems , 2004, Autom..

[4]  K. Gu An integral inequality in the stability problem of time-delay systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[5]  Lihua Xie,et al.  Further Improvement of Free-Weighting Matrices Technique for Systems With Time-Varying Delay , 2007, IEEE Transactions on Automatic Control.

[6]  Guo-Ping Liu,et al.  Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays , 2004, Syst. Control. Lett..

[7]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in System and Control Theory , 1994, Studies in Applied Mathematics.

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

[9]  M. Parlakçi Robust stability of uncertain time-varying state-delayed systems , 2006 .

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

[11]  V. Suplin,et al.  H/sub /spl infin// control of linear uncertain time-delay systems-a projection approach , 2006, IEEE Transactions on Automatic Control.

[12]  Min Wu,et al.  Augmented Lyapunov functional and delay‐dependent stability criteria for neutral systems , 2005 .

[13]  Jin-Hoon Kim,et al.  Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty , 2001, IEEE Trans. Autom. Control..

[14]  Tong Heng Lee,et al.  A less conservative robust stability test for linear uncertain time-delay systems , 2006, IEEE Trans. Autom. Control..

[15]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[16]  S. Niculescu Delay Effects on Stability: A Robust Control Approach , 2001 .

[17]  Y. Cao,et al.  Delay-dependent robust stabilization of uncertain systems with multiple state delays , 1998, IEEE Trans. Autom. Control..

[18]  Xi Li,et al.  Delay-dependent robust H control of uncertain linear state-delayed systems , 1999, Autom..

[19]  Yuechao Wang,et al.  An LMI approach to stability of systems with severe time-delay , 2004, IEEE Transactions on Automatic Control.

[20]  D. D. Perlmutter,et al.  Stability of time‐delay systems , 1972 .

[21]  Qing-Guo Wang,et al.  Delay-range-dependent stability for systems with time-varying delay , 2007, Autom..

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

[23]  Qing-Long Han A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays , 2004, Autom..