Stability Analysis of Time-Delay Systems

This chapter deals with the stability analysis of linear time-delay systems without and with parametric uncertainties. The stability analysis for both constant and time-varying delay in the states is considered. The focus of this chapter is to review the existing methods on delay-dependent stability analysis in an LMI framework based on Lyapunov-Krasovskii approach and consequently the improved results on delay-dependent stability analysis are presented. The results of the proposed techniques are validated by considering numerical examples and compared with existing results.

[1]  Qing-Long Han,et al.  On robust stability of neutral systems with time-varying discrete delay and norm-bounded uncertainty , 2004, Autom..

[2]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[3]  Hanyong Shao,et al.  Improved delay-dependent stability criteria for systems with a delay varying in a range , 2008, Autom..

[4]  Qing-Long Han,et al.  On Hinfinity control for linear systems with interval time-varying delay , 2005, Autom..

[5]  Shengyuan Xu,et al.  A survey of linear matrix inequality techniques in stability analysis of delay systems , 2008, Int. J. Syst. Sci..

[6]  Goshaidas Ray,et al.  Stability analysis for continuous system with additive time-varying delays: A less conservative result , 2010, Appl. Math. Comput..

[7]  Emilia Fridman,et al.  New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems , 2001, Syst. Control. Lett..

[8]  Vladimir L. Kharitonov,et al.  Additional dynamics for general class of time-delay systems , 2003, IEEE Trans. Autom. Control..

[9]  Silviu-Iulian Niculescu,et al.  Additional dynamics in transformed time-delay systems , 2000, IEEE Trans. Autom. Control..

[10]  Guo-Ping Liu,et al.  Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties , 2004, IEEE Transactions on Automatic Control.

[11]  G. Ray,et al.  Delay-dependent robust stability criteria for linear uncertain systems with interval time varying delay , 2009, TENCON 2009 - 2009 IEEE Region 10 Conference.

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

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

[14]  Goshaidas Ray,et al.  State feedback stabilization of uncertain linear time-delay systems: A nonlinear matrix inequality approach , 2011, Numer. Linear Algebra Appl..

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

[16]  C. Peng,et al.  Improved delay-dependent robust stability criteria for uncertain systems with interval time-varying delay , 2008 .

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

[18]  PooGyeon Park,et al.  A delay-dependent stability criterion for systems with uncertain time-invariant delays , 1999, IEEE Trans. Autom. Control..

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

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

[21]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..

[22]  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..

[23]  James Lam,et al.  A new delay system approach to network-based control , 2008, Autom..

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

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

[26]  C. Peng,et al.  Delay-dependent robust stability criteria for uncertain systems with interval time-varying delay , 2008 .

[27]  Huijun Gao,et al.  Stability analysis for continuous systems with two additive time-varying delay components , 2007, Syst. Control. Lett..

[28]  Delay-dependent stability analysis of linear system with multiple state delays , 2007, 2007 International Conference on Industrial and Information Systems.

[29]  C. D. Souza,et al.  Delay-dependent robust stability and stabilization of uncertain linear delay systems: a linear matrix inequality approach , 1997, IEEE Trans. Autom. Control..

[30]  Lianglin Xiong,et al.  Novel delay-dependent robust stability criteria for uncertain neutral systems with time-varying delay , 2009 .

[31]  Rifat Sipahi,et al.  An exact method for the stability analysis of time-delayed linear time-invariant (LTI) systems , 2002, IEEE Trans. Autom. Control..

[32]  Emilia Fridman,et al.  Parameter dependent stability and stabilization of uncertain time-delay systems , 2003, IEEE Trans. Autom. Control..

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

[34]  V. Kolmanovskii,et al.  On the Liapunov-Krasovskii functionals for stability analysis of linear delay systems , 1999 .

[35]  Hanyong Shao,et al.  New delay-dependent stability criteria for systems with interval delay , 2009, Autom..

[36]  Lei Guo,et al.  Delay‐range‐dependent robust stability and stabilization for uncertain systems with time‐varying delay , 2008 .

[37]  M. Parlakçi Improved robust stability criteria and design of robust stabilizing controller for uncertain linear time‐delay systems , 2006 .

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

[39]  Jean-Pierre Richard,et al.  Stability of some linear systems with delays , 1999, IEEE Trans. Autom. Control..

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

[41]  Guoping Liu,et al.  Improved delay-range-dependent stability criteria for linear systems with time-varying delays , 2010, Autom..

[42]  Silviu-Iulian Niculescu,et al.  On delay-dependent stability under model transformations of some neutral linear systems , 2001 .

[43]  PooGyeon Park,et al.  Stability and robust stability for systems with a time-varying delay , 2007, Autom..

[44]  Goshaidas Ray,et al.  DELAY-DEPENDENT STABILITY ANALYSIS OF LINEAR SYSTEM WITH TIME VARYING STATE DELAY , 2007 .

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

[46]  Te-Jen Su,et al.  Robust stability of interval time-delay systems with delay-dependence , 1998 .