Abstract By using a novel average dwell time approach, the stability problem for discrete-time switched systems with stable and unstable modes is investigated. First, the so-called weighted average dwell time is proposed and applied to reduce the conservativeness of stability results for the studied system whose all modes are stable. Then, combination the slow and fast weighted average dwell time, new stability criteria of discrete-time switched systems with some modes unstable are given. Third, by using linear matrix inequalities, the design of stabilizing controllers for discrete-time switched linear systems is presented. At last, two numerical examples illustrate that the new schemes have larger feasible regions for the design of switching signals than the existing results.

中文翻译：

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基于加权平均驻留时间法的具有稳定和不稳定模式的离散时间切换系统的稳定性分析

摘要 采用一种新颖的平均驻留时间方法，研究了具有稳定和不稳定模式的离散时间切换系统的稳定性问题。首先，提出并应用所谓的加权平均驻留时间来降低所有模态稳定的研究系统的稳定性结果的保守性。然后，结合慢速和快速加权平均驻留时间，给出了具有某些模态不稳定的离散时间切换系统的新稳定性判据。第三，利用线性矩阵不等式，提出了离散时间切换线性系统的稳定控制器的设计。最后，两个数值例子说明新方案比现有结果具有更大的开关信号设计可行域。