Integral sliding mode H$$_\infty $$ control of fractional system in presence of unmatched disturbance

Abstract

In this paper, $${H}_{\infty }$$ control for fractional order linear system in presence of unmatched disturbance is considered. Fractional order disturbance observer is designed to evaluate the unmatched disturbance. With choosing proper observer gain, the bounded convergence of the evaluated error is obtained. Afterwards an integral sliding mode surface is given on the basis of the disturbance estimation. Using linear matrix inequality technology, the state feedback controller is provided, which ensure the closed-loop system satisfy $${H}_{\infty }$$ performance. Finally, numerical example is given to illustrate the robustness of the designed control strategy.