Second-order predefined-time sliding-mode control of fractional-order systems

This paper presents a predefined-time control of fractional-order linear system subject to a large class of continuous but not necessarily integer-order differentiable disturbances. The dynamical system is based on the Caputo derivative and has an order that lies in (1,2). The proposed controller, based on a dynamic extension, induces an integer-order reaching phase, such that an invariant second-order sliding mode is enforced in predefined-time, that is, the solution of the fractional-order system and its integer-order derivative converge to the origin within a time that is prescribed as a tunable control parameter. The controller is continuous and able to compensate for unknown continuous disturbances. A simulation study is carried out in order to show the effectiveness of the proposed scheme.