LMI based design of a sliding mode controller for a class of uncertain fractional-order nonlinear systems

In this paper, the problem of designing a sliding mode controller for a class of uncertain fractional-order nonlinear systems with 0 <; β <; 1 is addressed by using linear matrix inequality (LMI) method. A key analysis technique is enabled by proposed a fundamental boundedness lemma, which is used for rigorous stability analysis of fractional-order systems, especially for Mittag-Leffler stability analysis of fractional-order nonlinear systems. A new switching law is given to guarantee the reachability condition. This sliding mode control law is utilized to obtain a controller capable of drawing the state trajectories onto the sliding surface and maintain the sliding motion. Numerical simulation results are presented to show the effectiveness of the proposed sliding mode control scheme.