Design of New Fractional Sliding Mode Control Due to Complete Synchronization of Commensurate and Incommensurate Fractional Order Chaotic Systems

Abstract

Synchronization between two nonlinear chaotic systems is an interesting problem in both theoretical as well as practical point of view. In this manuscript, the goal is introducing a fractional sliding surface and then design of a fractional sliding mode controller so as to synchronize two fractional nonlinear chaotic systems. The proposed method is performed to synchronize a class of fractional-order chaotic systems in the presence of uncertainties and external disturbances. Stability of the controlled system investigated and analysed by Lyapunov stability theory. The method applied on different example and numerical simulations are performed to show the applicability of the proposal. It is worth mentioning that the novel fractional sliding mode controller can be applied in order to control a broad range of fractional order dynamic systems.