In the past decades, semi-Markovian switching systems (S-MSSs) have received significant research attention in the systems and control community. S-MSSs, a special yet unique kind of stochastic switching systems, can be used to model and characterize a broad range of applications including modern communication technology, fault tolerant control, and DNA analysis. Different from Markovian switching systems, the transition rate in S-MSSs is jump-time dependent, which enables the capability of better capturing the practical behavior and modeling the physical systems, and meanwhile brings numerous challenges to the analysis and synthesis. The aim of this paper is to provide a comprehensive overview on recent theoretical development and advances of modeling, stability analysis, and control synthesis for S-MSSs. Researcher methodologies and results for S-MSSs on filter design, sliding mode control, finite-time control, and event-triggered control are systematically analyzed and summarized. Finally, some promising research directions and challenges for S-MSSs are presented.

在过去的几十年中，半马尔可夫交换系统（S-MSS）在系统和控制界受到了极大的研究关注。S-MSS 是一种特殊而独特的随机交换系统，可用于建模和表征广泛的应用，包括现代通信技术、容错控制和 DNA 分析。与马尔可夫交换系统不同，S-MSS 中的跃迁率依赖于跳跃时间，这使得能够更好地捕捉实际行为和对物理系统进行建模，同时也给分析和综合带来了诸多挑战。本文的目的是全面概述 S-MSS 建模、稳定性分析和控制综合的最新理论发展和进展。系统地分析和总结了 S-MSS 在滤波器设计、滑模控制、有限时间控制和事件触发控制方面的研究方法和结果。最后，提出了 S-MSS 的一些有前景的研究方向和挑战。