In the wave of advancements within the control theory field, a significant progress has been made in the precise models of complex systems. This development is crucial as it determines whether the theoretical methods under investigation can be effectively applied to real-world systems. Over the past few decades, practical systems have often been modeled as simple linear systems based on numerous assumptions that overlook the degradation of system components and the influence of environmental factors. Simple linear system models are becoming increasingly weak to deal with increasingly complex and changeable systems, especially, while inevitably facing sudden environmental disturbance, component maintenance and/or subsystem connection failure issues, all of which may lead to abrupt changes in system dynamics or structure, severely impacting the system’s dynamic behaviors. Markov stochastic processes are capable of characterizing the types of systems that experience dynamic or structural changes. The system governed by a Markov process is so-called Markov jump system (MJS), which can provide a clear framework for understanding and analyzing the dynamic behaviors of these systems, thereby enhancing the feasibility and effectiveness of control strategies. MJSs have long been a research hotspot in the control field and find widespread applications in robotic systems [1], wind power generation systems [2], economic systems [3], and aerospace systems [4].