Asynchronous control of continuous-time switched systems with all unstable modes under DoS attacks

In this article, the asynchronous control problem of switched linear systems with all unstable modes under denial-of-service (DoS) attacks is studied. First, the upper bound of the sampling period, which can be easily calculated based on the scenario where all modes are unstable, is obtained under a periodic sampling control strategy. Second, by constructing an appropriate discrete multiple linear quadratic Lyapunov function, an asynchronous control scheme in the form of linear matrix inequalities is devised. To ensure the stability of switched systems under DoS attacks, a sufficient condition for the total duration and frequency of DoS attacks is established. It is shown that the switched system can tolerate DoS attacks up to a certain limit while maintaining exponential stability, and this result is applicable even when all subsystems are unstable. Finally, numerical examples and a comparative study are presented to demonstrate the effectiveness of the proposed method.