A New Adaptive Robust Sliding Mode Control Approach for Nonlinear Singular Fractional-Order Systems

This article focuses on designing an adaptive sliding mode controller via state and output feedback for nonlinear singular fractional-order systems (SFOSs) with mismatched uncertainties. Firstly, on the basis of extending the dimension of the SFOS, a new integral sliding mode surface is constructed. Through this special sliding surface, the sliding mode of the descriptor system does not contain a singular matrix E. Then, the sufficient conditions that ensure the stability of sliding mode motion are given by using linear matrix inequality. Finally, the control law based on an adaptive mechanism that is used to update the nonlinear terms is designed to ensure the SFOS satisfies the reaching condition. The applicability of the proposed method is illustrated by a practical example of a fractional-order circuit system and two numerical examples.