Almost sure stability of Caputo fractional-order switched linear systems with deterministic and stochastic switching signals

Abstract

In this paper, we address the almost sure stability problem of Caputo fractional-order switched linear systems with deterministic and stochastic switching signals (DS-CFLSs). Firstly, due to the non-locality and memory of fractional-order switched systems, an inequality is proposed to solve the difficulties in the discussion of stability. Then, for DS-CFLSs, a deterministic switching strategy is predesigned, and stochastic switching signals are generated by the Markov process. After that, for the globally asymptotic stability almost surely (GAS a.s.) and exponential stability almost surely (ES a.s.) of DS-CFLSs, some sufficient conditions are proposed by using the multi-Lyapunov function and probability analysis methods. Finally, some numerical examples show that our results are effective.