Robust Exponential Stabilization for a Class of Nonlinear Uncertain Systems with Time-varying Delays

Abstract

This paper is concerned with the problem of robust exponential stabilization for a class of nonlinear uncertain systems with time-varying delays. By using appropriately chosen Lyapunov-Krasovskii functional, together with the Finsler’s lemma, sufficient conditions for exponential stability of nonlinear uncertain systems with time-varying delays are proposed in terms of linear matrix inequality (LMI). Then, novel sufficient conditions are developed to ensure the nonlinear uncertain system with time-varying delay is robust exponentially stabilizable in terms of linear matrix inequality with state feedback control. Finally, a numerical example is given to illustrate the efficiency of proposed methods.