Sliding mode control of fractional order nonlinear differential inclusion systems

Abstract

In this paper, variable structure control is utilized for stabilization of a particular class of nonlinear polytopic differential inclusion systems with fractional-order-0 < q < 1. By defining a sliding surface with fractional integral formula 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, the performance of the proposed method is illustrated with examples and related numerical simulations results.