Stability Analysis,Control Design And Applications Of Switched Chaotic System

In recent years,as an important branch of nonlinear science,chaotic systems and switched systems have been developed well,especially the combination of the two—the switched chaotic systems,which are more valuable than 'single chaotic systems and switched systems,especially in the areas of secure communication.This is because the security performance of communication will be improved with the switches of different structure chaotic systems.At present,the research of switched chaotic systems is not only rare,but also mainly concentrating on the problem of switched stabilization of the same dimension sub-systems.However,the different dimension chaotic sub-systems are usual in reality.So this paper will present a method which is called extend dimension method to investigate the switched chaotic systems which are combined with different dimension chaotic sub-systems.The first contribution of this paper is to propose a necessary and sufficient condition of the existence of control problem for the chaotic system.This condition ensures the realization of synchronization,anti-synchronization,the coexistence of synchronization and anti-synchronization,simultaneous synchronization and anti-synchronization,projective synchronization for chaotic systems.Further,the controller based on the method of like-linear feedback control is designed to achieve the control problem above.The second contribution of this paper is to construct the different dimension switched chaotic systems through the method of extend dimension method.Based on the achievements of single chaotic systems and switched systems,we investigate the control problems of switched chaotic systems through two ways:the switching path is arbitrary and the switching path is given.The third contribution of this paper is to research the simultaneous stabilization problems of the chaotic systems.Moreover,we compare the difference of switched stabilization on arbitrary path and simultaneous stabilization,and obtain some meaningful results.The first chapter of this paper is the introduction,which mainly introduces the research background,the current situation and the significance of the chaotic system,the switched system and the switched chaotic system.The second chapter of this paper is preliminaries,detailing the definition of control problem for chaotic systems,switched systems,and switched chaotic systems.Then we summarize the research methods of chaotic system and switched system,and give a necessary and sufficient condition of control problems for chaotic system,as well as the realization of control problem of some theorems and corollaries.The third chapter of this paper researches the construction of switched chaotic system and the stabilization problem.The author expounds the construction of switched chaotic system from the same dimensional chaotic sub-systems and the different dimension chaotic sub-system respectively.Furthermore,we compare the difference between switched stabilization on arbitrary path and simultaneous stabilization,and obtain some meaningful results.The fourth chapter mainly studies the control problems,including synchronization,anti-synchronization,the coexistence of synchronization and anti synchronization of such systems,simultaneous' synchronization and anti-synchronization,projective synchronization,and the numerical simulation verifies the validity and effectiveness of theoretical research.The fifth chapter includes the prospect and summary,which gives the innovation points,deficiencies and future research.