Protocol-Based SMC for Fuzzy Semi-Markov Switching Systems With Multizone Probabilitic Time-Varying Delays

Abstract

This study addresses the sliding mode control (SMC) for Takagi-Sugeno (T-S) fuzzy semi-Markov switching systems (FSMSSs) characterized by multizone probabilistic time-varying delays. The dynamic behaviors of FSMSSs are captured through a comprehensive semi-Markov process framework that accommodates arbitrary switching scenarios. In addition, a tailored SMC law that ensures the system’s trajectory reaches and maintains a preset sliding surface over a specified finite time is applied. To address the challenges of communication load, a novel multizone probabilistic dynamic event-triggered protocol is introduced, leveraging the time-varying nature of transmission delays and incorporating two adjustable internal dynamic variables. The establishment of sufficient conditions for ensuring the stochastic finite-time stability of the closed-loop system is achieved through an effective Lyapunov functional methodology. Finally, the validity and superiority of the proposed methodologies is demonstrated by a mass-spring-damper mechanical system.