Lyapunov function method for linear fractional order systems

Using the Lyapunov function method, this paper investigates the stability and the stabilization of linear fractional order systems, and presents a number of new results. First, some new properties of Caputo fractional derivative are presented. Then, a sufficient condition of asymptotical stability for fractional order systems is obtained by the Lyapunov function method. Furthermore, by designing state feedback controller for fractional order linear systems, asymptotical stabilization for closed-loop systems is considered. Finally, two illustrative examples are provided to illustrate main results.