Linear Matrix Inequality Based Fractional Integral Sliding-Mode Control of Uncertain Fractional-Order Nonlinear Systems

A design of linear matrix inequality (LMI)-based fractional-order surface for sliding-mode controller of a class of uncertain fractional-order nonlinear systems (FO-NSs) is proposed in this paper. A new switching law is achieved guaranteeing the reachability condition. This control law is established to obtain a sliding-mode controller (SMC) capable of deriving the state trajectories onto the fractional-order integral switching surface and maintain the sliding motion. Using LMIs, a sufficient condition for existence of the sliding surface is derived which ensures the t−α asymptotical stability on the sliding surface. Through a numerical example, the superior performance of the new fractional-order sliding mode controller is illustrated in comparison with a previously proposed method.