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. Note to Practitioners—In smart grid and power distribution systems, communication between remote sensors (e.g., voltage, current, and fault detectors) and controllers is often vulnerable to cyber threats such as DoS attacks. These attacks disrupt the timely of critical data, posing serious risks to system stability and performance. To address this challenge, a resilient asynchronous sampled-data control scheme is proposed. The scheme provides a practical solution to ensure stability in MJSs, even in the presence of data loss caused by DoS attacks. Theoretical tools such as discontinuous interval-dependent functionals and switched system stability analysis are employed to guide controller design, and the final outcome is an implementable control algorithm. The proposed method can be applied to enhance the security of industrial control systems, and it is well-suited for integration into modern power automation infrastructures to improve cyber-physical resilience.