Abstract

In this paper, the stabilization of coupled regime-switching jump diffusion with Markov switching topologies (CRJDM) is discussed. Particularly, we remove the restrictions that each of the switching subnetwork topologies is strongly connected or contains a directed spanning tree. Furthermore, a feedback control based on discrete-time state observations is proposed to make the CRJDM asymptotically stable. In most existing literature, feedback control only depends on discrete-time observations of state processes, while switching processes are observed continuously. Different from previous literature, feedback control depends on discrete-time observations of state processes as well as switching processes in this paper. Meanwhile, based on graph theory, stationary distribution of switching processes and Lyapunov method, some sufficient conditions are deduced to ensure the asymptotic stability of CRJDM. By applying the theoretical results to second-order oscillators with Markov switching topologies, a stability criterion is obtained. Finally, the effectiveness of the results is illustrated by a numerical example.

中文翻译：

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基于离散时间状态观测的反馈控制，用于基于马尔可夫切换拓扑的耦合态切换跳跃扩散的稳定

摘要

在本文中，讨论了具有马尔可夫开关拓扑（CRJDM）的耦合状态切换跳跃扩散的稳定性。特别是，我们消除了每个交换子网拓扑都牢固连接或包含定向生成树的限制。此外，提出了基于离散时间状态观测的反馈控制，以使CRJDM渐近稳定。在大多数现有文献中，反馈​​控制仅取决于状态过程的离散时间观察，而开关过程则是连续观察的。与以前的文献不同，反馈控制依赖于状态过程以及开关过程的离散时间观测。同时，基于图论，切换过程的平稳分布和李雅普诺夫方法，推导了一些足以保证CRJDM渐近稳定的条件。通过将理论结果应用于具有马尔可夫开关拓扑的二阶振荡器，可以获得稳定性判据。最后，通过数值例子说明了结果的有效性。