Stabilization of multi-input hybrid fractional-order systems with state delay

In this paper, the stabilization of a particular class of multi-input linear systems of fractional order differential inclusions with state delay using variable structure control is considered. First, the sliding surface with a fractional order integral formula is defined, and then the sufficient conditions for stability of the sliding surface are derived. Also, the concepts related to sliding control stabilization of differential inclusion systems with integer order are extended to differential inclusion systems with fractional order 0 < q < 1 . Furthermore, for stabilization of fractional order systems with delay in the state space, a feedback and the concept of the norm of a state space is exploited. Finally, simulation results are provided to show the effectiveness of the proposed method.