Multi-Surface Sliding Mode Controller for Stabilizing Uncertain Disturbed Fractional-Order Chaotic Systems

In this paper, a new multi-surface sliding mode controller is proposed for stabilizing both commensurate and non-commensurate general fractional order chaotic systems. New sliding surfaces are proposed and the related switching control law has been derived, analytically. The proposed multi-surface sliding mode controller with the new sliding surfaces, makes the states stable even in the presence of uncertainty and external disturbances. The stability of the closed loop system, in spite of uncertainty and disturbances in the system states, has been investigated via Lyapunov theory. Simulations have been performed to show the effectiveness of the proposed method for both commensurate and non-commensurate systems. Short settling time, low and smooth control effort and asymptotic stability of the states as well as the sliding surfaces are the performance features of the proposed controller.