Original scientific paper
https://doi.org/10.1080/00051144.2023.2262016
Almost sure stability of Caputo fractional-order switched linear systems with deterministic and stochastic switching signals
Qixiang Wang
; School of Electrical Engineering, Guizhou University, Guiyang, People’s Republic of China
Fei Long
; School of Artificial Intelligence and Electrical Engineering, Guizhou Institute of Technology, Guiyang, People’s Republic of China
Lipo Mo
; School of Mathematics and Statistics, Beijing Technology and Business University, Beijing, People’s Republic of China
Jing Yang
; School of Electrical Engineering, Guizhou University, Guiyang, People’s Republic of China
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.
Keywords
Caputo fractional-order switched systems; deterministic switching; stochastic switching; multi-Lyapunov functions; Markov process
Hrčak ID:
316006
URI
Publication date:
6.10.2023.
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