The stability of arbitrarily switched discrete-time linear singular (SDLS) systems is studied. Our analysis builds on the recently introduced one-step-map for SDLS systems of index-1. We first provide a sufficient stability condition in terms of Lyapunov functions. Furthermore, we generalize the notion of joint spectral radius of a finite set of matrix pairs, which allows us to fully characterize exponential stability.

中文翻译：

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切换离散时间线性奇异系统的稳定性分析

研究了任意切换离散时间线性奇异（SDLS）系统的稳定性。我们的分析建立在最近引入的索引为1的SDLS系统的一步图上。我们首先提供关于Lyapunov函数的充分稳定性条件。此外，我们推广了矩阵对的有限集合的联合谱半径的概念，这使我们能够充分表征指数稳定性。