Delay-dependent stability analysis of linear systems with time-varying delay

Stability analysis of linear systems with time- varying delay is investigated. In order to highlight the relations between the variation of the delay and the states, redundant equations are introduced to construct a new modeling of the delay system. New types of Lyapunov Krasovskii functionals are then proposed allowing to reduce the conservatism of the stability criterion. Delay dependent stability conditions are then formulated in terms of linear matrix inequalities (LMI). Finally, an example shows the effectiveness of the proposed methodology.

[1]  Chung-Yao Kao,et al.  Robust stability analysis of linear systems with time-varying delays , 2005 .

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

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

[4]  Adrian Stoica.  A unified algebraic approach to linear control design. R.E. Skelton, T. Iwasaki and K.M. Grigoriadis, Taylor & Francis, Ltd, London 1998, pp. IX+285, price £45. ISBN 0-7484-0592-5 , 2003 .

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

[6]  D. Peaucelle,et al.  Robust Performance Analysis of Linear Time-Invariant Uncertain Systems by Taking Higher-Order Time-Derivatives of the State , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[7]  Pierre-Alexandre Bliman,et al.  Lyapunov equation for the stability of linear delay systems of retarded and neutral type , 2002, IEEE Trans. Autom. Control..

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

[9]  F. Gouaisbaut,et al.  A NOTE ON STABILITY OF TIME DELAY SYSTEMS , 2006 .

[10]  Rifat Sipahi,et al.  Stability Robustness of Retarded LTI Systems with Single Delay and Exhaustive Determination of Their Imaginary Spectra , 2006, SIAM J. Control. Optim..

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

[12]  Dimitri Peaucelle,et al.  Discussion on: “Parameter-Dependent Lyapunov Function Approach to Stability Analysis and Design for Uncertain Systems with Time-Varying Delay” , 2005 .

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

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

[15]  F. Gouaisbaut,et al.  DELAY-DEPENDENT STABILITY ANALYSIS OF LINEAR TIME DELAY SYSTEMS , 2006 .

[16]  Springer. Niculescu,et al.  Delay effects on stability , 2001 .

[17]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[18]  F. Gouaisbaut,et al.  DELAY-DEPENDENT ROBUST STABILITY OF TIME DELAY SYSTEMS , 2006 .

[19]  A. H. Taub,et al.  Studies In Applied Mathematics , 1971 .

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

[21]  Dimitri Peaucelle,et al.  Quadratic separation for feedback connection of an uncertain matrix and an implicit linear transformation , 2007, Autom..

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

[23]  J. Zhang,et al.  Toward less conservative stability analysis of time-delay systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[24]  Emilia Fridman,et al.  Input-output approach to stability and L2-gain analysis of systems with time-varying delays , 2006, Syst. Control. Lett..

[25]  Panagiotis Tsiotras,et al.  Stability of time-delay systems: equivalence between Lyapunov and scaled small-gain conditions , 2001, IEEE Trans. Autom. Control..