Lyapunov-Type Criteria of Absorbing Continuous-Time Markov Chains

• 成果类型: Article
• 署名作者: Zhu, Shiyong; Li, Yuanyuan; Cao, Jinde; Dimirovski, Georgi M.; Lu, Jianquan
• 署名单位: Southeast University - China; City University of Hong Kong; Nanjing Forestry University; Southeast University - China; Yonsei University; Saints Cyril & Methodius University of Skopje
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3305354
• 发表日期: 2024
• 页码: 2422-2428
• 关键词: Asymptotic stability; continuous-time Markov chains (CT-MC); Lyapunov functions; sampled-data control

摘要

The Lyapunov stability theory is developed for absorbing continuous-time Markov chains (CT-MCs) in this technical note. The derived stability criteria are all necessary and sufficient for absorbing CT-MCs and set absorbing CT-MCs, where Lyapunov functions can be constructed in a polynomial amount of time with respect to the cardinality of state spaces. Furthermore, the gap between Lyapunov functions of the CT-MCs and of the discrete-time Markov chains is bridged by the feature that the length of the sampling period in the sampled-data CT-MCs does not affect the reachability. The results presented here provide a novel insight for efficient analysis and synthesis of large-scale CT-MCs in the same manner as in dynamic systems. The applicability of these novel theoretical results is demonstrated via practical bioinspired networks from the literature.