Stability analysis of time-delay systems A Lyapunov approach

International audience; This chapter is devoted to the stability problem of time-delay systems using time-domain approach. Some basic concepts of time-delay systems are introduced. Then some simple Lyapunov-Krasovskii funtionals complete Quadratic Lyapunov-Krasovskii functional and discretization scheme are introduced with connections and extent of conservatism compared. The issue of time-varying delays are also discussed. The concept of Razumikhin Theorem is introduced. An alternative model of coupled difference-differential equations and its stability problem are also introduced. © Springer-Verlag London Limited 2006.