Resilient Control of CPSs Under Mixed DoS Attacks: A Type-Dependent ADT Approach

This article studies the resilient control against mixed denial of service (DoS) attacks for cyber-physical systems (CPSs). Different from existing results, this work considers the presence of both zero- and hold-input attacks, where a unified model is introduced to describe mixed DoS attacks. Upon this model, the original CPS is reformulated as a switched system subject to a time-varying delay. To characterize the occurrence frequency and duration of zero- and hold-input attacks, the type-dependent average dwell time (ADT) switching is adopted. In the meantime, multiple discontinuous Lyapunov functions (MDLFs) suitable to the type-dependent ADT switching are employed. By virtue of the switching scheme and MDLFs, a piecewise feedback controller is designed to guarantee global uniform exponential stability and $H_\infty$ performance of the closed-loop system. In addition, the developed control law is extended to an observer-based version, accommodating the case when the system state is not fully measurable. Finally, the effectiveness of our theoretical results is verified by two numerical examples.