New stability criteria for linear time-delay systems using complete LKF method

This paper focuses on the stability test for linear systems with time-varying delay and provides new stability conditions in terms of linear matrix inequalities (LMIs). The basic idea is the use of complete Lyapunov–Krasovskii functional (LKF) method and the derivation employs the discretisation technique and the reciprocally convex combination. The main feature of this work lies in that the present result not only leads to some improvements over existing results in the LMI framework but also is applicable for time-delay systems with unstable delay-free case. Three numerical examples are given to show the effectiveness and merits of the present result.

[1]  PooGyeon Park,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011, Autom..

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

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

[4]  K. Gu,et al.  Stability of Linear Systems With Time‐Varying Delay: a Generalized Discretized Lyapunov Functional Approach , 2001 .

[5]  Qing-Long Han,et al.  A discrete delay decomposition approach to stability of linear retarded and neutral systems , 2009, Autom..

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

[7]  Fernando de Oliveira Souza,et al.  New delay-interval stability condition , 2014, Int. J. Syst. Sci..

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

[9]  Chang-Hua Lien,et al.  New stability criterion for a class of uncertain nonlinear neutral time-delay systems , 2001, Int. J. Syst. Sci..

[10]  Kun Liu,et al.  New conditions for delay-derivative-dependent stability , 2009, Autom..

[11]  Huaguang Zhang,et al.  Stability analysis for linear delayed systems via an optimally dividing delay interval approach , 2011, Autom..

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

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

[14]  Keqin Gu,et al.  Discretization schemes for Lyapunov-Krasovskii functionals in time-delay systems , 2001, Kybernetika.

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

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

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

[18]  Shengyuan Xu,et al.  On Equivalence and Efficiency of Certain Stability Criteria for Time-Delay Systems , 2007, IEEE Transactions on Automatic Control.

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

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

[21]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[22]  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).

[23]  Guang-Hong Yang,et al.  New results of stability analysis for systems with time‐varying delay , 2010 .

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

[25]  K. Gu.  A further refinement of discretized Lyapunov functional method for the stability of time-delay systems , 2001 .

[26]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

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

[28]  Qing-Long Han,et al.  New results for delay-dependent stability of linear systems with time-varying delay , 2002, Int. J. Syst. Sci..

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

[30]  Guang-Di Hu,et al.  Technical note Simple criteria for stability of neutral systems with multiple delays , 1997, Int. J. Syst. Sci..