Chaos Control And Chaos Synchronization Based On The Small Gain Theorem

Recently, chaos control and synchronization have been an active research of the nonlinear subject. This new technology promises to have a significant impact on many novel engineering applications. The challenging research field has become a scientific inter-discipline involving many other fields. At present, to realize chaos control and synchronization, many methods have been introduced, such as OGY method, adaptive control, sliding mode control, etc. These methods can be divided into two parts-linear control and nonlinear control. Nonetheless the methods using linear state feedback usually cannot guarantee globally stability; the nonlinear control laws usually are somewhat complex.In this paper, we study the small gain theorem. The control laws designed by this theorem are simpler, and globally stabilize the controlled system.Firstly, this paper introduces and summaries the research background, the research condition and the methods for the control and synchronization of the chaos systems. Subsequently, this paper introduces in detail a deep and valuable result in control theory, the well–known small gain theorem. Thirdly, we primarily study the chaos control of two new chaotic systems–Liu chaotic system, a 3-dimensional chaotic system. This new simpler controller is designed by virtue of the well-known small gain theorem, and the controlled systems are globally asymptotically stable. Compared with nonlinear controls, the linear controls have simpler structures and can be obtained more easily. Finally, on the one hand, the controller is given for the Liu system and Lorenz system based on the small gain theorem, on the other hand, the synchronization between a single scroll attractor chaotic system and Chen system is realized by using this theorem. Furthermore, the numerical simulation results verified the effectiveness of the method.