Advances on modeling and control of semi-Markovian switching systems: A Survey

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. (c) 2021 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.