Delay-dependent stability analysis for time delay system

An improved delay-dependent asymptotic stability condition for systems with time-varying delay in terms of a strict linear matrix inequality (LMI) is presented. Two slack matrix variables are introduced in the derivative of the Lyapunov-Krasovskii functional in order to reduce conservatism in existing delay-dependent stability conditions. When time-varying norm-bounded uncertainties appear in a system with time-varying delay, an improved robust delay-dependent stability condition is also given. Example demonstrates the reduced conservatism of the proposed approach.