Stability analysis of delayed fractional-order switched systems

Abstract

This paper discusses stability of delayed fractional-order switched systems. First, two useful propositions are proposed based on Razumikhin approach together with properties of fractional calculus and analytical techniques, which can well solve the difficulties caused by distributed and discrete delays and fractional-order derivatives. Then, with the help of multiple Lyapunov function approach and dwell time technique, an effective way is developed to overcome the trouble caused by switching rules. A delay-dependent dwell time is derived to guarantee asymptotic stability under the hypothesis that each subsystem of delayed fractional-order switched systems is asymptotically stable. Finally, two illustrative examples further clarify the obtained conclusions.