Dynamic Event-Triggered Asynchronous Fault Detection via Zonotopic Threshold Analysis for Fuzzy Hidden Markov Jump Systems Subject to Generally Hybrid Probabilities

This article addresses the asynchronous fault detection (FD) problem for fuzzy hidden Markov jump systems with generally hybrid probabilities under limited communication. To reduce network load, a novel bandwidth-aware dynamic event-triggered communication scheme (DETCS) is developed to transmit necessary sampled signals, where the threshold coefficient in the triggered protocol can be dynamically adjusted over time in accordance with both the system dynamics and bandwidth status. A multiple-hierarchical structure is constructed to simultaneously describe both the mismatch of premise variables due to the introduction of the DETCS and the mode asynchronization between the filter and the plant, where the mode asynchronization is fully characterized by a hidden Markov model with generally hybrid transition probabilities and mode detection probabilities. By applying the double variables-based decoupling principle and variable substitution principle, a co-design criterion for DETCS and optimal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathscr {L}_{\infty }/\mathscr {H}_{\infty }$</tex-math></inline-formula> asynchronous reduced-order FD filter in the finite-frequency domain is derived and given by an exact expression. Besides, unlike the constant thresholds in existing FD works, an innovative zonotope-based dynamic threshold strategy is developed for residual evaluation. Finally, two illustrative examples are utilized to verify the effectiveness of the proposed method.