SIAM Journal on Control and Optimization, Volume 59, Issue 2, Page 1188-1217, January 2021.
In this paper, the stability problem for a class of switched dynamic systems with logic switching signals is investigated. Emphasis is placed on the stability of logically switched dynamic systems (LSDSs) derived by using logic and switching rules. First, the so-called LSDSs giving a further extension of switched dynamic systems is designed for the first time, which is formulated in a hybrid form of a switched dynamic system and a logical dynamic system. Second, the concept of global uniform exponential stability is extended to the one for the LSDSs. It is illustrated that some traditional concepts of stability can be seen as special cases of the extended stability. Third, through the mode-dependent average dwell time (MDADT), average cycle dwell time (ACDT), stable cyclic sequence dependent average cycle dwell time (S-ACDT), and unstable cyclic sequence dependent average cycle dwell time (U-ACDT), the stability problem for LSDSs with all stable or partly stable subsystems is solved. In other words, based on multiple Lyapunov functions and a digital transformation approach, the stability criteria for LSDSs containing all stable subsystems or partially unstable subsystems are obtained in the nonlinear case. Correspondingly, the stability conditions for LSDSs are also derived in the linear case. Finally, two examples are presented to demonstrate the feasibility of the established results.

中文翻译：

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具有逻辑切换的动态切换系统及其稳定性分析

SIAM控制与优化杂志，第59卷，第2期，第1188-1217页，2021年1月。
本文研究了一类具有逻辑切换信号的切换动态系统的稳定性问题。重点放在通过使用逻辑和交换规则得出的逻辑交换动态系统（LSDS）的稳定性上。首先，首次设计了进一步扩展交换动态系统的所谓LSDS，它以交换动态系统和逻辑动态系统的混合形式制定。其次，全局一致指数稳定性的概念扩展到了LSDS的概念。说明了一些传统的稳定性概念可以看作是扩展稳定性的特殊情况。第三，通过模式相关的平均停留时间（MDADT），平均周期停留时间（ACDT），稳定的循环序列相关的平均周期停留时间（S-ACDT），以及依赖于不稳定的循环序列的平均循环停留时间（U-ACDT），解决了具有所有稳定或部分稳定子系统的LSDS的稳定性问题。换句话说，在非线性情况下，基于多个Lyapunov函数和一种数字转换方法，可以获得包含所有稳定子系统或部分不稳定子系统的LSDS的稳定性标准。相应地，在线性情况下也得出了LSDS的稳定性条件。最后，通过两个例子说明了所建立结果的可行性。在非线性情况下，获得了包含所有稳定子系统或部分不稳定子系统的LSDS的稳定性标准。相应地，在线性情况下也得出了LSDS的稳定性条件。最后，通过两个例子说明了所建立结果的可行性。在非线性情况下，获得了包含所有稳定子系统或部分不稳定子系统的LSDS的稳定性标准。相应地，在线性情况下也得出了LSDS的稳定性条件。最后，通过两个例子说明了所建立结果的可行性。