Dynamic Filtering for Semi‐Markov Jump Systems: A Threshold‐Dependent Approach

ABSTRACT This paper tackles the state estimation problem for semi‐Markov jump systems in unreliable communication environments, where challenges like state time delay, network congestion, and data loss arise. We propose a novel filtering framework that combines a dynamic event‐triggered mechanism with redundant communication channels. Unlike conventional methods, which ignore the impact of the triggering threshold on filtering performance, our approach explicitly accounts for this influence, improving state estimation accuracy. By leveraging a threshold‐dependent Lyapunov–Krasovskill functional and the properties of semi‐Markov signals, we establish an adaptive relationship between the threshold, triggering conditions, and filter gains, enhancing filtering performance during mode‐switching. To manage the complexity of infinite threshold‐dependent terms, we transform them into constant and time‐varying components. The effectiveness of our method is demonstrated through applications to a DC motor model and an RLC circuit system.