In this article, a unified mode‐dependent average dwell time (MDADT) stability result is investigated, which could be applied to switched systems with an arbitrary combination of stable and unstable subsystems. Combined with MDADT analysis method, we classified subsystems into two categories: switching stable subsystems and switching unstable subsystems. State divergence caused by switching unstable subsystems could be compensated by activating switching stable subsystems for a sufficiently long time. Based on the above considerations, a new globally exponentially stability condition was proposed for discrete‐time switched linear systems. Under the premise of not resolving the LMIs, the MDADT boundary of the new stability condition is allowed to be readjusted according to the actual switching signal. Furthermore, the new stability result is a generalization of the previous one, which is more suitable for the case of more unstable subsystems. Some simulation results are given to show the advantages of the theoretic results obtained.

中文翻译：

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离散时间切换系统的统一模式相关平均停留时间稳定性标准

在本文中，研究了统一的模式相关平均停留时间（MDADT）稳定性结果，该结果可应用于具有稳定和不稳定子系统的任意组合的交换系统。结合MDADT分析方法，将子系统分为两类：切换稳定子系统和切换不稳定子系统。可以通过在足够长的时间内激活切换稳定子系统来补偿由切换不稳定子系统引起的状态差异。基于以上考虑，针对离散时间线性切换系统提出了一种新的全局指数稳定性条件。在不解决LMI的前提下，允许根据实际切换信号重新调整新稳定条件的MDADT边界。此外，新的稳定性结果是对前一个结果的概括，它更适合于子系统更加不稳定的情况。给出了一些仿真结果，以显示所获得的理论结果的优势。