$H_{\infty}$ control against mixed DoS attacks for cyber-physical systems

This article focuses on the $H_{\infty}$ control against mixed denial of service (DoS) attacks for cyber-physical systems (CPSs), where attacks are under zero-input and hold-input strategies. By introducing a unified model describing the simultaneous existence of the two attacks, the CPS can be converted to a switched system with one delay. To ensure control performance, the type-dependent average dwell time (ADT) is applied for the first time to pose constraints on the occurrence frequency of DoS attacks. In the meantime, multiple discontinuous Lyapunov functions (MDLFs) are employed. Upon this, the global uniform exponential stability (GUES) and $H_{\infty}$ performance of the closed-loop system are guaranteed. Finally, the effectiveness of our theoretical results is verified by a numerical example.