Event‐triggered H∞ and reduced‐order asynchronous filtering for fuzzy Markov jump systems with time‐varying delays

The challenge of H∞$$ {H}_{\infty } $$ and asynchronous reduced‐order design for Takagi‐Sugeno (T‐S) fuzzy Markovian jump systems (MJSs) with time‐varying delays under the event‐triggered scheme (ETS) is investigated in this dissertation. A distributed event‐triggered strategy is provided on the basis of the specified triggering function to ensure consensus in the system, so effectively reducing data transmission. The existence conditions for a class of Markovian jump discrete‐time systems are determined. Unlike previous results, we present a novel membership function‐dependent fuzzy Lyapunov‐Krasovsikii (L‐K) functional with mode‐dependent integral terms, resulting in a stochastically stable filtering error system with the desired H∞$$ {H}_{\infty } $$ performance. By solving linear matrix inequality (LMIs), the recommended filter parameters are achieved. The proposed reduced‐order filter is demonstrated in numerical examples as effective as it is advantageous. Block diagram of the event‐triggered filtering system.