This paper proposes a new sequence-based approach to resolve the stability problems found in switched systems with unstable subsystems. In existing approaches, the sequence information of switching subsystems is seldom exploited. By exploiting the sequence information, threshold values can be less restrictive and more appropriate for the situation. We study two cases in this paper: (a) all subsystems are unstable, and (b) part of the subsystems are unstable. Both continuous-time and discrete-time systems are studied, and a numerical example is given to show the advantage of our approach.

中文翻译：

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具有不稳定子系统的开关系统的稳定性：基于序列的平均驻留时间方法

本文提出了一种新的基于序列的方法来解决在具有不稳定子系统的切换系统中发现的稳定性问题。在现有方法中，很少利用切换子系统的序列信息。通过利用序列信息，阈值可以减少限制并更适合这种情况。我们在本文中研究了两种情况：（a）所有子系统都不稳定，（b）部分子系统不稳定。研究了连续时间和离散时间系统，并给出了一个数值例子来展示我们方法的优势。