A delay decomposition approach to delay‐dependent stability for linear systems with time‐varying delays

This paper is concerned with delay‐dependent stability for linear systems with time‐varying delays. By decomposing the delay interval into multiple equidistant subintervals, on which different Lyapunov functionals are chosen, and new Lyapunov‐Krasvskii functionals are then constructed. Employing these new Lyapunov‐Krasvskii functionals, some new delay‐dependent stability criteria are established. The numerical examples show that the obtained results are less conservative than some existing ones in the literature. Copyright © 2009 John Wiley & Sons, Ltd.

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

[2]  Lihua Xie,et al.  Output feedback H∞ control of systems with parameter uncertainty , 1996 .

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

[4]  A. Luo,et al.  Discretized Lyapunov functional for systems with distributed delay and piecewise constant coefficients , 2001 .

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

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

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

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

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

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

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

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

[13]  Qing-Long Han,et al.  Absolute stability of time-delay systems with sector-bounded nonlinearity , 2005, Autom..

[14]  Pham Huu Anh Ngoc.  Strong stability radii of positive linear time‐delay systems , 2005 .

[15]  Qing-Long Han.  A new delay-dependent stability criterion for linear neutral systems with norm-bounded uncertainties in all system matrices , 2005, Int. J. Syst. Sci..

[16]  Yong He,et al.  Delay-dependent stabilization of linear systems with time-varying state and input delays , 2005, Autom..

[17]  Emilia Fridman,et al.  A new Lyapunov technique for robust control of systems with uncertain non-small delays , 2006, IMA J. Math. Control. Inf..

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

[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]  Zidong Wang,et al.  Robust H∞ control for a class of nonlinear stochastic systems with mixed time delay , 2007 .

[21]  Q. Han.  A delay decomposition approach to stability and H∞ control of linear time-delay systems — part I: Stability , 2008, 2008 7th World Congress on Intelligent Control and Automation.

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

[23]  J. Lam,et al.  An improved characterization of bounded realness for singular delay systems and its applications , 2008 .

[24]  Qing-Long Han,et al.  Robust Hinfinity filtering for a class of uncertain linear systems with time-varying delay , 2008, Autom..