Resilient asynchronous sampled-data control for Markov jump systems under DoS attacks: A discontinuous interval-dependent Lyapunov functional

This article investigates the security control problem of Markov jump systems (MJSs) under denial of service (DoS) attacks by constructing a class of discontinuous interval-dependent functional. Motivated by (1) the enhanced practicality and flexibility of multi-sensor sampled-data control with asynchronous packet arrivals and (2) the destabilizing impact of DoS-induced data loss, a resilient asynchronous sampled-data control (RASDC) scheme is designed. RASDC can send data once immediately after the attack, thereby alleviating the performance degradation caused by long-term no input. Furthermore, by utilizing the stability analysis idea of switched systems, a discontinuous interval-dependent functional is constructed, which combines the information of the resilient sampling interval and the attack interval. To overcome the analytical challenges posed by its discontinuities, the discrete-time Lyapunov stability theory, convex combination techniques, and some estimation methods are used to derive the sufficient condition for mean square asymptotic stability. In light of the stability criterion, a design algorithm for the secure controller is provided. Finally, simulation results demonstrate the effectiveness of the proposed approach.