Hidden Markov Jump Systems: Event-Triggered Control against Deception Attacks under Restricted Information Flow

In industrial scenarios, networked control systems often encounter narrow bandwidth bottlenecks and deception attacks. Traditional periodic sampling strategies send packets at fixed intervals, which is redundant, and they assume that modes are fully observable and dwell times follow an exponential distribution, making it difficult to handle the combined uncertainties of 'non-periodic sampling, random attacks, and mode loss.' At the moment of mode switching, attackers inject false signals through hidden paths, causing frequent false alarms and missed detections with fixed-threshold detectors, leading to rapid deterioration of closed-loop performance. This paper studies event-triggered secure control of hidden semi-Markov jump systems: first, it models both the sampling interval and attack duration as a hidden semiMarkov chain with general distribution to capture spatiotemporal coupling; then, it proposes residual-based adaptive threshold triggering, communicating only when residuals exceed limits, significantly reducing the burden. A mode-estimation-dependent composite Lyapunov function is constructed, and by using posterior probabilities and dwell-time information, LMI conditions ensuring stochastic H∞ performance are derived, enabling a oneshot co-design of the observer, controller, and triggering weights. Simulation and water tank experiments verify that the proposed method achieves fewer communications, lower peaks, and faster detection under the same security level, providing new insights for secure control in resource-constrained environments.