Control And Synchronization Of A Class Of Fractional-Order Chaotic Systems Via Linear Controller

In recent years, fractional order calculus has gradually become a new branch of applied science field. But, due to a lack of clear physical significance and geometrical explanation and its complexity, it is rarely used to solve the practical problems encountered in physics and engineering for long time. Related researches just stay on the basis of the mathematical theory and develop slowly. Until the seventy’s last century, the fractional order calculus has attracted lots of attention in many fields of science and engineering. Due to its powerful advantage and broad application prospects, it has widely been applied in control theory, mathematics, nonlinear science, chemical engineering science, biological engineering science and many other fields.In the field of control theory, the stability and control of the fractional order nonlinear systems have been the research focus and difficulty. This paper focuses on a class of the fractional order chaotic system, mainly concerns on the stability, control and synchronous controller design. A series of conditions for ensuring stability and the method for stabilization and synchronization controller design are presented. The main contents include:(1) A stability theory of a class of fractional order differential nonlinear system is presented, On this basis, a appropriate linear feedback controller is designed to achieve the stabilization of such systems. Only discussing and controlling the linear parts, without making any changes on the nonlinear parts, which has good theory meaning and project application value. Theoretical proof and experimental results show that the feasibility and effectiveness of the conclusions.(2) Synchronization control for a class of fractional-order chaotic systems is discussed. Based on the stability theory of fractional-order system, an appropriate linear feedback controller is designed to achieve the synchronization of a class of fractional order chaotic systems. Theoretical proof and numerical simulation examples verify the correctness and effectiveness of the proposed method.Finally,this paper is concluded with the outlook for the future.