On eigenvalue sets and convergence rate of Itô stochastic systems with Markovian switching
On eigenvalue sets and convergence rate of Itô stochastic systems with Markovian switching
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DOI：
10.1109/tac.2010.2085630
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发表时间：
2010-07
期刊：
影响因子：
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通讯作者：
Zhao‐Yan Li;Bin Zhou;Yong Wang;G. Duan
中科院分区：
文献类型：
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作者：
Zhao‐Yan Li;Bin Zhou;Yong Wang;G. Duan
研究了一类具有马尔可夫切换的伊藤随机系统的稳定性分析和镇定问题。定义了一对正算子的特征值集，用以刻画随机系统在均方意义下的稳定性。这些特征值集的性质建立的基础上，我们表明，这些特征值集的谱横坐标是相同的，因此这些特征值集是等价的，在这个意义上表征系统的稳定性。同时，证明了马尔可夫跳Itô随机系统的保收敛速度可以由某个特征值集决定.最后，提出了一种基于线性矩阵不等式的方法来设计控制器，使得闭环系统具有保证的收敛速度。数值算例验证了该方法的有效性。本文的研究为未来的工作开辟了几个角度，作为一些开放的问题。
This paper is concerned with stability analysis and stabilization of Itô stochastic systems with Markovian switching. A couple of eigenvalue sets for some positive operator associated with the stochastic system under study are defined to characterize its stability in the mean square sense. Properties for these eigenvalue sets are established based on which we show that the spectral abscissa of these eigenvalues sets are the same and thus these eigenvalue sets are equivalent in the sense of characterizing the stability of the system. Also, it is shown that the guaranteed convergence rate of the Markovian jump Itô stochastic systems can be determined by some eigenvalue set. Finally, a linear matrix inequality based approach is proposed to design controllers such that the closed-loop system has guaranteed convergence rate. Some numerical examples are carried out to illustrate the effectiveness of the proposed approach. The research in this paper opens several perspectives for future work stated as some open problems.