LMI Based Synchronization Control of Nonlinear Affine Fractional Order Chaotic Systems Considering Input Constraint

Abstract

This paper deals with synchronization problem of chaotic nonlinear fractional order systems with input saturation constraint. To develop the idea, at first a generlized sector condition and a memory-less nonlinear function are employed to deal with the saturation problem. Then a new state feedback controller is designed to achieve synchronization in master-slave chaotic fractional order nonlinear systems with input saturation. The stability of the closed-loop system is guaranteed using Lyapunov theory and sufficient stability conditions are formulated in terms of caputo fractional derivative of a quadratic Lyapunov function and Linear Matrix Inequalities (LMI) . Finally, to verify the effectiveness of the proposed control scheme, some simulation results are employed to show the effectiveness of the proposed methodology.