PI-Type Sliding Mode Fractional-Order Synchronization of a Memristive Chua Circuit

In this study, a sliding mode fractional-order synchronization is proposed for the memristive chaotic Chua system. After the integer-order model of the chaotic memristive Chua system is given, a PI-type sliding surface-based controller structure combined with the fractional derivative operator is devised. The stability analysis of the synchronization closed-loop system is proven in the sense of Lyapunov theory. To demonstrate the effectiveness and applicability of the proposed controller structure, the fractional-order derivative operator in the controller structure is considered with two different fractional orders, and computer-based numerical simulation studies are performed comparatively.