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.

在本文中，切换线性系统的输入到状态稳定性（ISS）问题在拒绝服务（DoS）攻击和外部干扰下研究了不稳定模式。与仅考虑稳定模式并且通常对切换行为和DoS攻击施加某些约束的早期结果相比，研究了具有不稳定模式的切换系统，并提出了一种灵活的描述来指定不稳定模式。此外，更一般的情况被认为是允许在DoS攻击活动期间进行切换，攻击可以独立于切换任意发生。因此，它可以更好地描述 DoS 攻击下的切换系统和更一般的结果。此外，在采样方案和 DoS 攻击下，会出现异步问题。尽管有这些额外的并发症，推导了一个关于DoS攻击频率和持续时间的充分条件，以确保系统在DoS攻击下的ISS，结果揭示了不稳定模式的平均时间比例与系统抵抗DoS攻击的弹性之间的权衡。最后通过数值算例和对比研究证明了所提方法的有效性。