Dynamic Event-Triggered Filtering of Semi-Markov Jump System with Time-Varying Delay

This paper explores dynamic event-triggered filtering for a class of semi-Markov jump systems with time-varying delays. Utilizing the semi-Markov kernel, we analyze these systems and design a dynamic event-triggering mechanism to alleviate communication pressure. A Lyapunov function is constructed with a guaranteed negative trigger threshold. After a period of dwell time, the system undergoes mode transitions. By ensuring that the Lyapunov function decays during this process, we derive a set of sufficient conditions for the existence of the filter under the dynamic event-triggering mechanism. Finally, a numerical example is provided to verify the effectiveness of the proposed method.