Input-to-state stability of switched linear systems with unstabilizable modes under DoS attacks

Yan-Wu Wang, Ze-Hong Zeng, Xiaokang Liu, Zhi-Wei Liu

Abstract: In this paper, the input-to-state stability (ISS) problem of switched linear system with unstabilizable modes is investigated under denial-of-service (DoS) attacks and external disturbance. In contrast to earlier results which consider only stabilizable modes and usually impose certain constraints on the switching behavior and the DoS attacks, the switched system with unstabilizable modes is studied and a flexible description is proposed to specify the unstabilizable modes. Besides, a more general situation is considered that it allows switching during the active period of DoS attack and the attacks can take place arbitrarily independent of switching. Thus, it leads to a better description of switched system under DoS attacks and a more general result. Moreover, under the sampling scheme and DoS attacks, the asynchronous problem arises. Despite these added complications, a sufficient condition concerning DoS attacks frequency and duration is derived to ensure the ISS of the system under DoS attacks, and the result reveals the trade-off between the average time proportion of unstabilizable modes and the resilience of the system against DoS attacks. Finally, a numerical example and a comparative study are given to show the effectiveness of the proposed method.