A switching signal for a switched system is said to be shuffled if all modes of the system are activated infinitely often. In this paper, we develop tools to analyze stability properties of discrete-time switched linear systems driven by shuffled switching signals. We introduce the new notion of shuffled joint spectral radius (SJSR), which intuitively measures how much the state of the system contracts each time the signal shuffles (i.e. each time all modes have been activated). We show how this notion relates to stability properties of the associated switched systems. In particular, we show that some switched systems that are unstable for arbitrary switching signals can be stabilized by using switching signals that shuffle sufficiently fast and that the SJSR allows us to derive an expression of the minimal shuffling rate required to stabilize the system. We then present several approaches to compute lower and upper bounds of the SJSR using tools such as the classical joint spectral radius, Lyapunov functions and finite state automata. Several tightness results of the bounds are established. Finally, numerical experiments are presented to illustrate the main results of the paper.

如果系统的所有模式都被无限频繁地激活，则称用于切换系统的切换信号被洗牌。在本文中，我们开发了工具来分析由混洗开关信号驱动的离散时间开关线性系统的稳定性特性。我们引入了混洗联合谱半径的新概念（SJSR），它直观地测量每次信号洗牌时系统的状态收缩多少（即每次所有模式都被激活时）。我们展示了这个概念如何与相关切换系统的稳定性属性相关联。特别是，我们展示了一些对于任意切换信号不稳定的切换系统可以通过使用足够快的切换信号来稳定，并且 SJSR 允许我们推导出稳定系统所需的最小切换速率的表达式。然后，我们提出了几种使用经典联合谱半径、Lyapunov 函数和有限状态自动机等工具来计算 SJSR 下限和上限的方法。建立了几个边界的紧密度结果。最后，