Stabilization of a Class of Uncertain Nonlinear System via Fractional Sliding Mode Controller

In this paper, a novel fractional sliding mode control scheme is suggested to stabilize a second-order uncertain nonlinear system. The proposed sliding manifolds, which will converge to the origin in finite time by utilizing a classical quadratic Lyapunov function, ensures the reduction of the chattering phenomenon during the control process. Based on Lyapunov's stability theorem, the closed-loop system can be stabilized to the origin in the future time. Some results about the control and stabilization of such nonlinear systems, when the fractional sliding mode controller is used, are illustrated in this paper. Finally, an example with numerical simulations is provided to show the validity and feasibility of the proposed method.