Fractional-Order Sliding Mode Control Method for a Class of Integer-Order Nonlinear Systems

In this study, the problem of the stabilisation of a class of nonautonomous nonlinear systems was studied. First, a fractional stability theorem based on a fractional-order Lyapunov inequality was formulated. Then, a novel fractional-order sliding surface, which was a generalisation of integral, first-order, and second-order sliding surfaces with varying fractional orders, was proposed. Finally, a fractional-order sliding mode-based control for a class of nonlinear systems was designed. The stability property of the system with the proposed method was easily proven as a fractional Lyapunov direct method by the fractional stability theorem. As an illustration, the method was used as a fractional guidance law with an impact angle constraint for a manoeuvring target. Simulation results demonstrated the applicability and efficiency of the proposed method.