Equivalent Stability Notions, Lyapunov Inequality, and Its Application in Discrete-Time Linear Systems With Stochastic Dynamics Determined by an i.i.d.?Process
Equivalent Stability Notions, Lyapunov Inequality, and Its Application in Discrete-Time Linear Systems With Stochastic Dynamics Determined by an i.i.d.?Process
复制标题
等效稳定性概念、李亚普诺夫不等式及其在由独立同分布过程确定的随机动力学离散时间线性系统中的应用
DOI：
10.1109/tac.2019.2905216
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发表时间：
2019
影响因子：
6.8
通讯作者：
Hagiwara Tomomichi
中科院分区：
文献类型：
--
作者：
Hosoe Yohei;Hagiwara Tomomichi
本文研究离散时间线性随机动态系统的稳定性分析与综合。等价性首先证明了三个稳定的概念下的一些关键假设的随机性背后的系统。特别是，我们使用的假设，确定系统动态的随机过程是独立的，相同的离散时间分布。然后，一个李雅普诺夫不等式条件的必要和充分意义下的稳定性。虽然我们的李雅普诺夫不等式将涉及包含在期望运算中的决策变量，但提供了一种思想来解决它作为一个标准的线性矩阵不等式，该思想也发挥了重要作用的状态反馈综合的基础上的李雅普诺夫不等式。激励数值例子进一步讨论作为我们的方法的应用。
This paper is concerned with stability analysis and synthesis for discrete-time linear systems with stochastic dynamics. Equivalence is first proved for three stability notions under some key assumptions on the randomness behind the systems. In particular, we use the assumption that the stochastic process determining the system dynamics is independent and identically distributed with respect to the discrete time. Then, a Lyapunov inequality condition is derived for stability in a necessary and sufficient sense. Although our Lyapunov inequality will involve decision variables contained in the expectation operation, an idea is provided to solve it as a standard linear matrix inequality; the idea also plays an important role in state feedback synthesis based on the Lyapunov inequality. Motivating numerical examples are further discussed as an application of our approach.