Stability Analysis and Design of Impulsive Control Systems With Time Delay

A class of impulsive control systems with time-varying delays is considered. By establishing an impulsive delay differential inequality, we analyze the global exponential stability of the impulsive delay systems and estimate the exponential convergence rate. On the basis of the analysis, a design procedure of impulsive controller is presented. The designed impulsive controller not only can globally exponentially stabilize the time delay systems, but also can control the exponential convergence rate of the systems. Two numerical examples are given to illustrate the effectiveness of the method.

I. Introduction

Stabilization problem of linear or nonlinear dynamic systems with time delay is receiving much attention. The existence of a delay in a nonlinear system may induce more complex dynamical behaviors such as instability, oscillations, and chaos, e.g., in Mackey-Glass model [1] and Chua's circuit system with delay [2]. Some important control methods have been developed for stabilizing dynamic systems without delay or with delay, which include state feedback control [3], [4], adaptive control [5], fuzzy control [6], variable structure control [7], etc.