The Control And Synchronization Of Chaotic Systems With Discontinuous Output (Input)

In this thesis,we mainly consider the control and synchronization of chaotic systems with discontinuous output(input).It is well known that in reality not all of the state variables are available for some chaotic systems and the transmitted signal may be interrupted for some reasons.Therefore,the research of the control and synchronization of chaotic systems with discontinuous output(input)is of great theoretical and practical significance.This thesis investigates the control and synchronization of chaotic systems with discontinuous output(input)and some sufficient conditions are derived.The numerical simulations are presented to verify the effectiveness of the proposed method.Besides,based on the combination synchronization scheme a new type of synchronization: the equal combination synchronization is proposed.This thesis is categorized into five parts and the organization is as follows:In the first chapter,some typical definitions of chaos synchronization and approaches commonly used in chaotic synchronization are introduced,also,the main contents of this thesis are briefed.In the second chapter,we study the synchronization of a class of chaotic systems with discontinuous output.The drive system is assumed that only the output state variable is available and the output may be a discontinuous state variable.By constructing proper response system,some novel criteria of synchronization are proposed.The new chaotic system proposed by Cai is taken as an example to justify our results.Chapter 3 first proposes a new type of synchronization: the equal combination synchronization and then investigates the equal combination synchronization of a class of chaotic systems.By assuming that only the output state variable is available and the output may be discontinuous state variable some novel criteria for the equal combination synchronization are proposed via constructing proper observers.The Lorenz chaotic system is taken as an example to demonstrate the efficiency of the proposed approach.The control and synchronization of a class of chaotic systems with discontinuous input is studied in Chapter 4.Based on the stability theory some novel criteria forcontrol and synchronization of the chaotic systems are proposed.The Lorenz chaotic system is taken as an example to demonstrate the effectiveness of the proposed schemes.In the fifth chapter,the research work of this thesis is summarized and the possible direction is further proposed.