In this paper, the stability issue for a class of cyclic switched linear systems with all stable or partly unstable submodes is investigated. Firstly, the new concepts of stable cyclic sequence-dependent cycle dwell time (S-CDT) and unstable cyclic sequence-dependent cycle dwell time (U-CDT) are proposed for the first time. Then, based on linear matrix inequalities (multiple Lyapunov functions) and cycle dwell time (CDT) switching law, the stability conditions for slowly cyclic switched linear (nonlinear) systems with all stable submodes are established. Furthermore, by using linear matrix inequalities (multiple Lyapunov functions), S-CDT and U-CDT switching laws, the stability criteria are derived for slowly and fastly cyclic switched linear (nonlinear) systems with a designed cyclic switching scheme where slow S-CDT switching and fast U-CDT switching are, respectively, applied to partly stable and partly unstable submodes. Finally, three numerical examples are presented to demonstrate the feasibility of the developed results.

本文研究了一类具有全部稳定或部分不稳定子模态的循环切换线性系统的稳定性问题。首先，首次提出了稳定循环序列相关循环停留时间（S-CDT）和不稳定循环序列相关循环停留时间（U-CDT）的新概念。然后，基于线性矩阵不等式（多个Lyapunov函数）和循环驻留时间（CDT）切换律，建立了具有所有稳定子模态的慢循环切换线性（非线性）系统的稳定性条件。此外，通过使用线性矩阵不等式（多个 Lyapunov 函数）、S-CDT 和 U-CDT 切换定律，稳定性标准是针对具有设计循环切换方案的慢速和快速循环切换线性（非线性）系统得出的，其中慢速 S-CDT 切换和快速 U-CDT 切换分别应用于部分稳定和部分不稳定的子模式。最后，给出了三个数值例子来证明所开发结果的可行性。