Sign-stability of Positive Markov Jump Linear Systems
Sign-stability of Positive Markov Jump Linear Systems
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DOI：
10.1016/j.automatica.2019.108638
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
J. Cavalcanti;H. Balakrishnan
中科院分区：
文献类型：
--
作者：
J. Cavalcanti;H. Balakrishnan
本文研究了没有数值实现的正马尔可夫跳变线性系统的稳定性。它考虑了子系统矩阵和马尔可夫转移矩阵的元素只有符号（而不是量）已知的情况。结果是对稳定性的定性概念的分析，称为符号稳定性。虽然pmjls的符号稳定性概念是指数几乎确定、平均和均方稳定等标准随机稳定性概念的自然扩展，但符号稳定性概念被证明是等价的，而它们对应的标准概念则不是这样。此外，对于不可约的马尔可夫链，证明了马尔可夫链的特殊结构与符号稳定性无关。
This paper investigates stability of Positive Markov Jump Linear Systems (PMJLSs) in the absence of a numerical realization. It considers the situation when only signs (and not magnitudes) of the entries of the subsystem matrices and the Markov transition matrices are known. The result is an analysis of a qualitative notion of stability known as sign-stability. Although the notions of sign-stability of PMJLSs are natural extensions of standard stochastic stability concepts such as exponential almost sure, mean and mean-square stability, the sign-stability notions are proven equivalent, which is not the case for their corresponding standard concepts. Moreover, for irreducible Markov chains, the particular structure of the Markov chain is shown to have no bearing on sign-stability.