Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities
Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities
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DOI：
10.1016/j.automatica.2008.08.010
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发表时间：
2009-02
期刊：
影响因子：
--
通讯作者：
Lixian Zhang;E. Boukas
中科院分区：
文献类型：
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作者：
Lixian Zhang;E. Boukas
研究了一类转移概率部分未知的连续时间和离散时间马尔可夫跳跃线性系统(MJLS)的稳定性和镇定问题。所考虑的系统是更一般的系统，它将转移概率完全已知和完全未知的系统作为两种特殊情况--后者是任意切换下的切换线性系统。此外，与最近研究的不确定转移概率相比，本文提出的部分未知转移概率的概念不需要任何未知元素的知识。利用LMIS方法给出了基本系统随机稳定和镇定的充分条件，并通过提出的混杂系统揭示了目前所得到的一般MJLS稳定性判据与任意切换下切换线性系统的稳定性判据之间的关系。文中给出了两个数值算例，验证了所得结果的有效性和潜力。
In this paper, the stability and stabilization problems of a class of continuous-time and discrete-time Markovian jump linear system (MJLS) with partly unknown transition probabilities are investigated. The system under consideration is more general, which covers the systems with completely known and completely unknown transition probabilities as two special cases — the latter is hereby the switched linear systems under arbitrary switching. Moreover, in contrast with the uncertain transition probabilities studied recently, the concept of partly unknown transition probabilities proposed in this paper does not require any knowledge of the unknown elements. The sufficient conditions for stochastic stability and stabilization of the underlying systems are derived via LMIs formulation, and the relation between the stability criteria currently obtained for the usual MJLS and switched linear systems under arbitrary switching, are exposed by the proposed class of hybrid systems. Two numerical examples are given to show the validity and potential of the developed results.