Asymptotical stabilization of nonlinear uncertain fractional-order system

In this article, we give the sufficient conditions of the state feedback stabilization for the nonlinear uncertain fractional-order system (FOS) with the fractional-order 0 <; α <; 1. The key is to design suitable state feedback controller that guarantees the stability of the closed-loop control system. By applying the Fractional Lyapunov direct method, a new result via the linear matrix inequality (LMI) is obtained for the state feedback controller synthesis of the FOS. Finally, a numerical example is given to show the validity and superiority of the proposed design method.