Dynamic event-based finite-time mixed H∞ and passive asynchronous filtering for T–S fuzzy singular Markov jump systems with general transition rates

Abstract In this paper, the design of finite-time mixed H ∞ and passive asynchronous filter for T–S fuzzy singular Markov jump systems with general transition rates under the dynamic event-based scheme is discussed. An asynchronous filter is considered such that the phenomena of asynchronous modes between the original singular Markov jump systems and the considered filter is modelled as a hidden Markov model. A dynamic event-based scheme is proposed to further mitigate the network transmission burden. By augmenting the states of the original singular Markov jump systems and the constructed asynchronous filter, the filtering error system is transformed into a singular time-delay Markov jump system. Based on the Lyapunov–Krasovskii functional concerning the internal dynamic variable, the criteria of stochastically admissible and stochastically finite-time boundness with the given mixed H ∞ and passivity performance index for the filtering error system are subject to linear matrix inequalities and several constraint conditions. Furthermore, the unified co-design approach of the desired asynchronous filter and the proposed dynamic event-based strategy is developed. Finally, a numerical instance is employed to demonstrate the correctness and effectiveness of the developed technique.