The input-to-state stability (ISS) for a class of discrete hybrid time-delay systems with admissible edge-dependent average dwell time (AED-ADT) is investigated in this study. By using the Lyapunov-like functions, the conditions for ISS are derived under the following situations: all subsystems are stable, all subsystems are unstable, and some subsystems are unstable. When all the continuous subsystems are ISS, although the impulsive effects are destabilizing, the system is ISS with respect to a lower bound of AED-ADT. Moreover, when all the subsystems are not ISS, the impulsive effects can still successfully stabilize the system for an upper bound of AED-ADT. When some continuous subsystems are not ISS, the impulsive effects can also successfully stabilize the system with a lower bound of AED-ADT under specific conditions. For the special case in which the Lyapunov-like function is allowed to decrease and increase during the operation time of a certain mode, a fresh transformation scheme of the Lyapunov-like functions is used to address the difficulty caused by the external input. A connection is established among AED-ADT, impulses magnitude, the interval length of increase of the Lyapunov function, and decaying/increasing rates of the Lyapunov function, such that the impulsive switched delayed system is ISS. The conclusions can be applied to a large class of systems because the transformation technique fills the gap between special and general cases. Finally, an example is provided, and simulations are performed to confirm the validity of the main results.

本研究研究了一类具有容许边缘相关平均驻留时间 (AED-ADT) 的离散混合时滞系统的输入状态稳定性 (ISS)。利用类李雅普诺夫函数，推导出以下情况下ISS的条件：所有子系统稳定，所有子系统不稳定，部分子系统不稳定。当所有连续子系统都是 ISS 时，虽然脉冲效应是不稳定的，但系统相对于 AED-ADT 的下界是 ISS。此外，当所有子系统都不是 ISS 时，脉冲效应仍然可以成功地稳定系统以达到 AED-ADT 的上限。当一些连续子系统不是 ISS 时，脉冲效应也可以在特定条件下以 AED-ADT 的下限成功稳定系统。对于在某种模态的运算时间内允许类李雅普诺夫函数增减的特殊情况，采用了类李雅普诺夫函数的新变换方案来解决外部输入带来的困难。建立AED-ADT、脉冲幅度、Lyapunov函数增加的区间长度和Lyapunov函数的衰减/增加率之间的联系，使得脉冲切换延迟系统为ISS。结论可以应用于一大类系统，因为转换技术填补了特殊情况和一般情况之间的空白。最后给出了一个例子，并通过仿真验证了主要结果的有效性。