Mode Cluster-Based Event-Triggered Control for Stochastic Markovian Jump Systems Under Denial-of-Service Attack

This article investigates the mode cluster-based event-triggered control (MCETC) of stochastic Markovian jump systems (SMJSs) under denial-of-service (DoS) attack. First, a novel MCETC framework is designed by considering the interplay among subsystems, DoS attacks, and the event-triggered mechanism (ETM). In this framework, the controller mode is reconstructed, and the number of controller modes is reduced by reclustering the system modes. It significantly reduces the conservatism of the system compared to existing mode-dependent/-independent controllers. Second, a switching ETM is designed for scenarios with and without DoS attack activation, which can effectively save network bandwidth resources and reduce computational load. Third, a multi-Lyapunov function based on DoS attacks is proposed to ensure the stability of the closed-loop SMJSs. Then, the controller gains and event-triggered parameters are jointly solved via the linear matrix inequality (LMI) technique. Moreover, the maximum allowable sampling interval (MASI) is given such that the controller can restore the control signals as soon as a DoS attack ends, which enables faster stabilization of the closed-loop system. Finally, a numerical example is used to verify the effectiveness and superiority of the proposed method.