Analysis and Synthesis of Markov Jump Linear Systems With Time-Varying Delays and Partially Known Transition Probabilities
Analysis and Synthesis of Markov Jump Linear Systems With Time-Varying Delays and Partially Known Transition Probabilities
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DOI：
10.1109/tac.2008.2007867
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发表时间：
2008-11
影响因子：
6.8
通讯作者：
Lixian Zhang;E. Boukas;J. Lam
中科院分区：
文献类型：
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作者：
Lixian Zhang;E. Boukas;J. Lam
研究了一类转移概率部分已知且具有时变时滞的离散Markov跳变线性系统的稳定性分析与镇定问题。时间延迟被认为是时变的，并有一个下限和上限。该模型将模式跳变的转移概率看作是部分已知的，从而放宽了马尔可夫跳变系统中所有模式跳变的转移概率必须完全先验已知的传统假设.在最近的研究中，一类系统的单调性进一步观察到的保守性，由于转移概率矩阵中的未知元素获得的最大延迟范围。利用线性矩阵不等式（LMI）方法给出了系统随机稳定的充分条件，并进一步给出了镇定控制器的设计。数值例子来说明所发展的理论。
In this note, the stability analysis and stabilization problems for a class of discrete-time Markov jump linear systems with partially known transition probabilities and time-varying delays are investigated. The time-delay is considered to be time-varying and has a lower and upper bounds. The transition probabilities of the mode jumps are considered to be partially known, which relax the traditional assumption in Markov jump systems that all of them must be completely known a priori. Following the recent study on the class of systems, a monotonicity is further observed in concern of the conservatism of obtaining the maximal delay range due to the unknown elements in the transition probability matrix. Sufficient conditions for stochastic stability of the underlying systems are derived via the linear matrix inequality (LMI) formulation, and the design of the stabilizing controller is further given. A numerical example is used to illustrate the developed theory.