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

Abstract

The current paper deals with synchronization problem among chaotic nonlinear fractional order systems considering input saturation constraint. To develop the idea, at first a generalized 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. Using the state feedback controller, the asymptotic stability of whole dynamic error model between master and slave is achieved. 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.

Keywords

Input Affine system / chaos systems / input saturation / nonlinear fractional order / feedback controller / synchronization

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