A non-smooth stochastic Lyapunov function and its relationship with viscosity solutions
A non-smooth stochastic Lyapunov function and its relationship with viscosity solutions
复制标题
非光滑随机李亚普诺夫函数及其与粘度解的关系
DOI：
10.1109/ascc.2017.8287255
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Hoshino Kenta
中科院分区：
文献类型：
--
作者：
Nishimura Yuki;Hoshino Kenta
本文利用一类在某些点上不光滑的随机李雅普诺夫函数的特殊形状，给出了随机系统的原点在某些意义下稳定的充分条件。处理的稳定性性质是瞬态稳定性和瞬态渐近稳定的起源是非平衡，和稳定性的概率和概率渐近稳定的起源是平衡。此外，我们还讨论了我们的随机李雅普诺夫函数和粘性上解之间的关系，这是经常用于分析确定性系统的非光滑李雅普诺夫函数的概念。然后，我们提出了一个宽松的概念，粘性弱上解的随机李雅普诺夫函数。
In this paper, we derive sufficient conditions that the origin of a stochastic system is stable in some meanings by a particular shape of a stochastic Lyapunov function without smoothness at some points. The treated stability properties are transient stability and transient asymptotic stability for the origins being non-equilibria, and stability in probability and asymptotic stability in probability for the origins being equilibria. Furthermore, we also discuss the relationship between our stochastic Lyapunov functions and viscosity supersolutions, which are the notion often used for analyzing non-smooth Lyapunov functions for deterministic systems. Then, we propose a relaxed notion of viscosity weak supersolution for our stochastic Lyapunov function.