Exponential stabilization of uncertain nonlinear time-delay systems

Abstract

This paper is concerned with the problem of exponential stabilization for a class of uncertain nonlinear systems with state delay by means of periodically intermittent control. Based on the Lyapunov-Krasovskii functional approach, several sufficient conditions of exponential stabilization for this class of uncertain nonlinear systems with state delay are proposed, which have been expressed in terms of linear matrix inequalities (LMIs) whose feasibility can be easily checked by using the numerically efficient Matlab LMI Toolbox. Further, the control design method is extended to a class of nonlinear systems with state delay. And the new stability criterion is also presented, which guarantees the closed-loop systems are exponentially stable. Finally, two numerical examples are given to show the effectiveness of the proposed approach. MSC:93D15, 93C55, 34K20, 34D23.