Stability and stabilization of fractional-order non-autonomous systems with unbounded delay

The stability and stabilization of a kind of fractional-order systems with unbounded delay is studied in this paper. A new fractional-order derivative inequality for convex function is established by means of the properties of absolutely continuous function, which extends some existing results. A new Razumikhin-type Lyapunov theorem is proved based on the auxiliary function and comparison principle. Different from the existing results, this Razumikhin-type Lyapunov theorem can be applied directly to the stability analysis of the fractional-order system with unbounded delay (FOSUD). By using this theorem, several stability and stabilization criteria for the FOSUD are established. To exemplify the utility of these criteria, three numerical examples are presented. • One new fractional-order derivative inequality for convex functions has been proved in the right-hand upper Dini derivative case. • One new Razumikhin-type Lyapunov theorem has been given for fractional-order systems with unbounded delay. • The stability and stabilization of a kind of fractional-order nonautonomous system with unbounded delay have been studied. The validity of the new Razumikhin-type Lyapunov theorem has been verified.