A survey of linear matrix inequality techniques in stability analysis of delay systems

Abstract

Recent years have witnessed a resurgence of research interests in analysing the stability of time-delay systems. Many results have been reported using a variety of approaches and techniques. However, much of the focus has been laid on the use of the Lyapunov–Krasovskii theory to derive sufficient stability conditions in the form of linear matrix inequalities. The purpose of this article is to survey the recent results developed to analyse the asymptotic stability of time-delay systems. Both delay-independent and delay-dependent results are reported in the article. Special emphases are given to the issues of conservatism of the results and computational complexity. Connections of certain delay-dependent stability results are also discussed.

Keywords:

• delay-independent stability
• delay-dependent stability
• linear matrix inequality
• time-delay systems

Acknowledgements

This work is supported by RGC HKU 7029/05P, the National Science Foundation for Distinguished Young Scholars of P.R. China under Grant 60625303, the Program for New Century Excellent Talents in University (No. NCET-04-0508), and the Specialised Research Fund for the Doctoral Program of Higher Education under Grant 20060288021.