Dynamic Event-Triggered Sliding Mode Control of Discrete-Time Markov Jump Systems with Actuator Saturation

The article delves into the dynamic event-triggered sliding mode control (SMC) of discrete-time Markov jump systems (MJSs), emphasizing the critical issue of actuator saturation. It begins by highlighting the versatility of MJSs in modeling dynamic systems with catastrophic characteristics, citing applications in communication networks, circuit systems, mathematical finance, and mechanical engineering. The study addresses the need for robust control methods in the presence of actuator saturation, which can degrade system performance and lead to instability if not properly managed. The authors propose a dynamic event-triggered mechanism (DETM) that effectively saves communication resources and enhances system robustness. A mode-based sliding mode surface (SMS) is introduced, and strict linear matrix inequality (LMI) conditions are derived to ensure stochastic stability performance. The article also presents an optimization method to estimate the domain of attraction, providing a practical approach to ensure system stability. Through detailed illustrative examples, the effectiveness of the proposed methods is demonstrated, showcasing improved control strategies and reduced communication loads compared to static event-triggered mechanisms. The conclusions underscore the superiority of the suggested approach and outline future directions for advanced event-triggered mechanisms.