Quantization-Based Event-Triggering Fault Detection Filtering for T–S Fuzzy Singular Semi-Markovian Jump Systems Against Multi-cyber-attacks

This paper delves into the problem of asynchronous fault detection filter (AFDF) for Takagi–Sugeno (T–S) fuzzy singular semi-Markovian jump systems (FSSJSs) with multi-cyber-attacks via dynamic event-triggering mechanism (ETM) and double-quantized schemes (DQS). First, a new design structure is devised by integrating the ETM and DQS into a unified framework to effectively alleviate the communication pressure. In particular, the event-triggered threshold (ETT) is dynamically regulated in line with system information, and not only the data from the plant to the filter but also that from the filter to the plant, are both quantized using different logarithmic quantizers. Second, the hybrid cyber-attacks platform is adopted, of which including the random deception attacks (DAs), random replay attacks (RAs) and DoS attack. Third, leveraging the principles of Lyapunov theory, some sufficient conditions are derived to guarantee the exponential admissibility (EA) of the resulting error dynamics and their adherence to a prescribed \(\mathcal {H}_{\infty }\) ${\mathcal{H}}_{\infty }$ performance index. Through the utilization of several matrix inequalities, the desired filtering gains are given. Finally, the effectiveness of the achieved results is demonstrated by two examples.