Stochastic stability of Positive Markov Jump Linear Systems
Stochastic stability of Positive Markov Jump Linear Systems
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DOI：
10.1016/j.automatica.2014.02.016
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发表时间：
2014-04
期刊：
影响因子：
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通讯作者：
P. Bolzern;P. Colaneri;G. Nicolao
中科院分区：
文献类型：
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作者：
P. Bolzern;P. Colaneri;G. Nicolao
本文研究了正马尔可夫跳变线性系统（PMJLS），即具有非负状态变量的马尔可夫跳变线性系统的稳定性。这些系统的具体特点突出。特别是，一个新的概念的稳定性（指数平均稳定性）的介绍，并证明是等价的标准概念的1时刻稳定。在不同的保守性程度下，给出了指数几乎必然稳定的充分条件。不同的稳定性概念之间的影响进行了讨论。值得注意的是，由于正性假设，一些条件可以通过求解线性规划可行性问题来检查。
This paper investigates on the stability properties of Positive Markov Jump Linear Systems (PMJLS’s), i.e. Markov Jump Linear Systems with nonnegative state variables. Specific features of these systems are highlighted. In particular, a new notion of stability (Exponential Mean stability) is introduced and is shown to be equivalent to the standard notion of 1-moment stability. Moreover, various sufficient conditions for Exponential Almost-Sure stability are worked out, with different levels of conservatism. The implications among the different stability notions are discussed. It is remarkable that, thanks to the positivity assumption, some conditions can be checked by solving Linear Programming feasibility problems.