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.