Stability Analysis And Synchronization Control Of Fractional Nonlinear Systems

In recent years, with the leap forward development of computer science and technology, and fractional calculus theories are becoming more mature, fractional-order calculus as extension of integer order calculus in order have attracted the attention of many scholars both at home and abroad. Due to its powerful advantage and broad application prospects in many aspects such as physics, chemistry, biology and engineering, fractional calculus has become immediate research focus. Especially, stability and control of the fractional-order nonlinear systemare the hot and difficult topic. This paper focuses on several typical fractional-order nonlinear systems, including fractional-order semilinear system, fractional-order complex network, fractional-order chaotic system and fractional-order (delayed) neural network, mainly concerns on stability, stabilization 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. Stability and stabilization problems for a class of semilinear fractional-order systemsare are considered. Based on the stability theorem of fractional-order linear system, Mittag-Leffler function, Laplace transform, Gronwall inequality as well as inequality scaling skills, by estimating analytical solutions expression of system. 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 for a class of fractional order hyper chaotic systems with unknown parameters is studied. Based on the stability theory of fractional order systems and by using the quadratic Lyapunov function, the synchronization controller and recognizing rules are designed for synchronizing the fractional order hyper chaotic Chen system and fractional order hyper chaotic Lorenz system. The final results of the numerical simulation showed that the control method proposed in this paper is feasible.3. Finite-time stable theorem about fractional order chaotic system and finite-time synchronizing fractional chaotic system are studied. By Putting forward a group a decision methods about the finite-time stability of the nonlinear fractional order chaotic systems that based on the stability theory of the Lyapunov fractional order. We design the synchronization controller by using this kind of method with the condition of all the systems variables with bounded then realized the finite-time synchronization of the drive system and response system. Simulation results verify the proposed control method.