Stabilization a class of fractional-order polytopic differential inclusion systems and variable structure control

In this paper, sliding mode control is utilized for stabilization of a particular class of polytopic differential inclusion systems with fractional-order-0<;q<;1. By defining a sliding surface with fractional integral formula, exploiting the concept of the norm of the state space, and obtaining sufficient conditions for stability of the sliding surface, a special feedback law is presented which enables the system states to reach the sliding surface and consequently creates a sliding mode control. Finally, performance of the method is illustrated using example and simulations.