Sufficient conditions of observer-based control for nonlinear fractional-order systems

In this article, we presents a method based on the state observer design for a class of nonlinear fractional-order systems (FOSs) with the fractional-order 0 <; α <; 1. The asymptotic stability conditions of closed-loop control nonlinear systems are derived by Fractional Lyapunov direct method. The observer gain matrix and control gain matrix are obtained in terms of linear matrix inequalities (LMIs) formulation. Finally, a numerical example of fractional-order chaotic Lorenz systems is given to demonstrate the applicability of proposed approach.