A novel event-triggered asynchronous H∞ control for T-S fuzzy Markov jump systems under hidden Markov switching topologies

Abstract This paper investigates the network-based H ∞ control problem for Takagi-Sugeno fuzzy Markov jump systems with communication delays. Firstly, we propose a novel mode-dependent event-triggered communication scheme (ETCS) based on aperiodically sampled data, which largely reduce the data transmission. Secondly, to obtain a more applicable result, an asynchronous controller based on a hidden Markov model is designed for the first time to stabilize the fuzzy Markov jump systems with general transition rates. Thirdly, a less restrictive Lyapunov-Krasovskii functional, which is discontinuous and only required to be positive definite at endpoints of each subinterval of the holding intervals, is newly introduced for event-triggered asynchronous control issue. Based on the above methods, sufficient conditions with less conservatism are obtained to ensure the stochastic stability of the resulting closed-loop systems with a prescribed H ∞ performance. A co-design method of the desired controller and ETCS is then presented. Finally, truck-trailer model and mass-spring-damper model are provided to demonstrate the effectiveness and practicability of the developed results.