Exponential stabilization of uncertain nonlinear time-delay systems

Yali Dong,Jinying Liu

doi:10.1186/1687-1847-2012-180

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

Highlights

Time delay naturally appears in many control systems and is frequently a source of instability [ – ]
We investigate the problem of exponential stabilization for a class of uncertain nonlinear systems by using another in-continuous feedback, i.e., periodically intermittent control
Motivated by the aforementioned discussion, in this paper, we study a class of intermittent control with time duration for a class of uncertain nonlinear time-delay systems

Summary

Introduction

Time delay naturally appears in many control systems and is frequently a source of instability [ – ]. We investigate the problem of exponential stabilization for a class of uncertain nonlinear systems by using another in-continuous feedback, i.e., periodically intermittent control. In [ ], the authors investigated the exponential stabilization problem for a class of chaotic systems with delay by means of periodically intermittent control.

Results

Conclusion