Fractional-order switching type control law design for adaptive sliding mode technique of 3D fractional-order nonlinear systems

In this article, an adaptive sliding mode technique based on a fractional-order (FO) switching type control law is designed to guarantee robust stability for a class of uncertain three-dimensional FO nonlinear systems with external disturbance. A novel FO switching type control law is proposed to ensure the existence of the sliding motion in finite time. Appropriate adaptive laws are shown to tackle the uncertainty and external disturbance. The calculation formula of the reaching time is analyzed and computed. The reachability analysis is visualized to show how to obtain a shorter reaching time. A stability criteria of the FO sliding mode dynamics is derived based on indirect approach to Lyapunov stability. Effectiveness of the proposed control scheme is illustrated through numerical simulations. (c) 2015 Wiley Periodicals, Inc. Complexity 21: 363-373, 2016