The Fuzzy Impulsive Control And Synchronization Of Chaotic Systems

Chaos control and synchronization are new fields in explorations of chaotic motions, and it is crucial in applications of chaos.In this paper,by constructing different controllers, the non-time-delayed impulsive control and synchronization,the time-delayed and equidistant impulsive control and synchronization as well as the generally time-delayed impulsive control and synchronization of chaotic systems based on T-S fuzzy model are studied,respectively.The main contents in this paper can be summarized as follows:The first section is introduction,in which we present research background,purpose and significance of chaos and chaos control,and then the research status quo and results of chaos control and synchronization are given.Finally the organization of this paper is also presented.The T-S fuzzy model and T-S fuzzy control system of chaotic system are introduced in Section 2.In Section 3,the fuzzy and non-time-delayed impulsive control and synchronization of chaotic systems are discussed.Some sufficient conditions ensuring the globally asymptotical stability and exponential stability of chaotic system are obtained by designing a non-time-delayed impulsive controller based on T-S fuzzy control model,respectively. And then,the asymptotical synchronization criteria of chaotic systems are also given by using similar research methods.Finally,some numerical examples and simulations are presented to show the feasibility and effectiveness of the proposed methods.The fuzzy and time-delayed equidistant impulsive control and synchronization of chaotic systems are investigated in Section 4,and here,the feedback delay is equivalent to the impulsive interval.Some new and sufficient conditions ensuring the globally asymptotical stability and exponential stability of chaotic systems are derived by constructing a feedback time-delayed equidistant impulsive controller and employing the impulsive differential equation theory based on T-S fuzzy control model.And then,the asymptotical synchronization criteria of chaotic systems are also given.Finally,some numerical simulations are presented to verify the obtained results.In section 5,a general feedback time-delayed fuzzy impulsive controller is designed for chaotic systems,and some sufficient criteria to guarantee the uniformly asymptotical stability and uniformly asymptotical synchronization of chaotic systems based on T-S fuzzy model are derived.This is the first time to study the uniformly asymptotical stability and synchronization under the fuzzy impulsive control,the results obtained in this section are new and useful verified through some numerical simulations.