Stochastic stability properties of jump linear systems
Stochastic stability properties of jump linear systems
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DOI：
10.1109/9.109637
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发表时间：
1992
影响因子：
6.8
通讯作者：
Xiangbo Feng;K. Loparo;Y. Ji;H. Chizeck
中科院分区：
文献类型：
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作者：
Xiangbo Feng;K. Loparo;Y. Ji;H. Chizeck
跳跃线性系统被定义为具有随机跳跃参数（通常由马尔可夫跳跃过程控制）的一系列线性系统，用于对遭受故障或结构变化的系统进行建模。作者研究了跳跃线性系统中的随机稳定性特性以及各种力矩和样本路径稳定性特性之间的关系。结果表明，所有二阶矩稳定性性质都是等效的，并且足以保证几乎确定的样本路径稳定性，并推导了二阶矩稳定性的可检验的充分必要条件。讨论了研究几乎确定样本稳定性的李雅普诺夫指数方法，并提出了表征跳跃线性系统李雅普诺夫指数的定理。最后，对于一维跳跃线性系统，证明了δ矩稳定性区域单调收敛于δ向下箭头0/sup +/处的几乎确定稳定性区域。 >
Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented. Finally, for one-dimensional jump linear system, it is proved that the region for delta -moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0/sup +/. >