Robust stability of uncertain singularly perturbed systems with time-varying delay

The problem of robust stability for a class of uncertain singularly perturbed systems with time-varying delay is presented. A new delay dependent stability criteria is devised by a method converting the singularly perturbed systems into a descriptor system equivalently. Then a Lyapunov-Krasovskii function is proposed. The delay dependent stability sufficient condition for the descriptor system is obtained with linear matrix inequality method. A numerical example is given to illustrate the efficacy of the proposed approach.