Design of Static Output Feedback Sliding Mode Control for Fractional Order Uncertain Linear Systems ⋆

This paper presents the problem of designing a sliding mode controller via static output feedback for a class of fractional order time-varying mismatched uncertain systems, in which all states are unavailable and estimated states are not required. On the basis of auxiliary system, a sliding mode control law with output feedback characteristics is researched by studying the structure decomposition of fractional order systems. Based on fractional order Lyapunov stability theorem, a switching surface is designed by using linear matrix inequality (LMI) method. Then we further consider a synthesis control law such that the motion of the closed loop system satisfies the reaching condition. Moreover, numerical simulations are performed to confirm the effectiveness and feasibility of the proposed control scheme.