General Stability of Stochastic Markov Jump Linear Systems Based on the Spectrum Technique
General Stability of Stochastic Markov Jump Linear Systems Based on the Spectrum Technique
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DOI：
10.1002/asjc.710
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发表时间：
2013-09
影响因子：
2.4
通讯作者：
Li Sheng;Ming Gao;Weihai Zhang
中科院分区：
文献类型：
--
作者：
Li Sheng;Ming Gao;Weihai Zhang
本文应用谱方法研究了随机马尔可夫跳变线性系统的广义稳定性。首先，定义了SMJLS的谱概念，揭示了谱与渐近均方稳定性之间的关系。其次，通过对复平面上谱分布的分析，引入了临界稳定性、区域稳定性和本质不稳定性等新的稳定性概念。建立了这种广义稳定性的充分必要条件。最后，通过数值算例验证了理论的正确性.
This paper applies the spectrum technique to investigate the general stability of stochastic Markov jump linear systems (SMJLSs). First, the notion of spectrum for SMJLSs is defined and the relationship between the spectrum and the asymptotical mean square stability is revealed. Second, by analyzing the spectrum distribution in the complex plane, some new concepts of stability, such as critical stability, regional stability, and essential instability, are introduced for SMJLSs. Necessary and sufficient conditions on such general stability are established. Finally, several numerical examples are carried out to illustrate the developed theory.