Memory-Based Event-Triggered Control of Markov Jump Systems Under Hybrid Cyber Attacks: A Switching-Like Adaptive Law

This paper investigates the security control of a class of discrete-time Markov jump systems (DMJS). Due to the vulnerability of open communication networks to cyber attacks, a hybrid attack model is established to describe the situation where the DMJS is simultaneously suffered from deception attacks (DAs) and denial-of-service (DoS) attacks. To cope with the intermittent characteristic of DoS attacks, adaptive memory-based event-triggered control (AMETC) with a switching-like adaptive law is proposed. The designed AMETC includes historical triggered data in its triggering condition, hence allows data transmission to adjust adaptively based on the long-term change of system state. In addition, when DoS attacks are launched by attackers, the designed switching-like adaptive law can help decrease the threshold to trigger more sampled data so as to stabilize the DMJS. These features contribute to improve the tolerance of the whole control system to DoS attacks and DAs. On the basis of the AMETC, a novel Lyapunov functional is designed, and sufficient conditions are derived to ensure the asymptotic stability of DMJSs. This functional plays a crucial role in ensuring the negative definiteness of the LMIs in the stability condition. Based on the stability condition, a design algorithm for security control gains and event-trigger matrices is given. Finally, simulation results validate the effectiveness and superiority of the proposed mechanism.