Exponential mean-square stabilization control for cyber-physical systems under random DoS attacks and transmission delay

In this paper, we address the problem of exponential mean-square stabilization control for cyber-physical systems (CPSs) characterized by time-varying parameters, random denial-of-service (DoS) attacks, and transmission delay. The motivation arises from the increasing complexity and vulnerability of CPSs, which are prone to various networked challenges, including random DoS attacks and transmission delays. Additionally, the presence of time-varying parameters further exacerbates the difficulty in designing stabilizing control strategies. To tackle this challenging issue, we propose two distinct approaches. First, we utilize the frozen technique, leading to the derivation of two explicit sufficient conditions. This technique exploits the concept of “freezing” the time-varying system parameters, providing an novel way to circumvent the construction of Lyapunov functions. The second method involves extending the generalized spectral radius to CPSs for the first time, allowing us to obtain an easily computable adjoint spectral radius. With this extension, we establish necessary and sufficient conditions for achieving exponential stabilization. The effectiveness of our proposed methods are illustrated through two simulation examples.