Lyapunov-Type Criteria of Absorbing Continuous-Time Markov Chains

被引：2
|
作者：
Zhu, Shiyong [1 ,2 ]
Li, Yuanyuan [3 ]
Cao, Jinde [4 ,5 ]
Dimirovski, Georgi M. [6 ]
Lu, Jianquan [1 ]
机构：
[1] Southeast Univ, Sch Math, Dept Syst Sci, Nanjing 210096, Peoples R China
[2] City Univ Hong Kong, Dept Elect Engn, Dept Syst Sci, Hong Kong, Peoples R China
[3] Nanjing Forestry Univ, Dept Appl Math, Nanjing 210037, Peoples R China
[4] Southeast Univ, Frontiers Sci Ctr Mobile Informat Commun & Secur, Sch Math, Nanjing 210096, Peoples R China
[5] Yonsei Univ, Yonsei Frontier Lab, Seoul 03722, South Korea
[6] SS Cyril & Methodius Univ Skopje, Doctoral Sch FEIT, MKD-1000 Skopje, North Macedonia
来源：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2024年 / 69卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Asymptotic stability; continuous-time Markov chains (CT-MC); Lyapunov functions; sampled-data control; FEEDBACK STABILIZATION; BOOLEAN NETWORKS; STABILITY;
D O I：
10.1109/TAC.2023.3305354
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
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.
引用
收藏
页码：2422 / 2428
页数：7
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