论文标题
随机开关系统的几乎确定的稳定性：基于图升力的方法
Almost sure Stability of Stochastic Switched Systems: Graph lifts-based Approach
论文作者
论文摘要
在本文中，我们开发了工具，以建立随机开关系统的稳定性，其开关信号受自动机的约束。在随机图的设置中提供了现有结果的必要概括之后，我们根据多个Lyapunov函数提供了几乎确定稳定性的表征。我们介绍了升降机的概念，提供了随机图的正式扩展，并保证保留了潜在的概率框架。我们展示了这些技术首先在确定性设置中引入的如何提供层次方法，以计算几乎确定的衰减率的紧密上限。最终通过数值示例说明了理论发展。
In this paper, we develop tools to establish almost sure stability of stochastic switched systems whose switching signal is constrained by an automaton. After having provided the necessary generalizations of existing results in the setting of stochastic graphs, we provide a characterization of almost sure stability in terms of multiple Lyapunov functions. We introduce the concept of lifts, providing formal expansions of stochastic graphs, together with the guarantee of conserving the underlying probability framework. We show how these techniques, firstly introduced in the deterministic setting, provide hierarchical methods in order to compute tight upper bounds for the almost sure decay rate. The theoretical developments are finally illustrated via a numerical example.
