This paper deals with learning stability of partially observed switched linear systems under arbitrary switching. Such systems are widely used to describe cyber–physical systems which arise by combining physical systems with digital components. In many real-world applications, the internal states cannot be observed directly. It is thus more realistic to conduct system analysis using the outputs of the system. Stability is one of the most frequent requirement for safety and robustness of cyber–physical systems. Existing methods for analyzing stability of switched linear systems often require the knowledge of the parameters and/or all the states of the underlying system. In this paper, we propose an algorithm for deciding stability of switched linear systems under arbitrary switching based purely on observed output data. The proposed algorithm essentially relies on an output-based Lyapunov stability framework and returns an estimate of the joint spectral radius (JSR). We also prove a probably approximately correct error bound on the quality of the estimate of the JSR from the perspective of statistical learning theory.

中文翻译：

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部分观察的切换线性系统的学习稳定性

本文研究了任意切换下部分观察的切换线性系统的学习稳定性。此类系统广泛用于描述通过将物理系统与数字组件相结合而产生的网络物理系统。在许多实际应用中，内部状态无法直接观察。因此，使用系统的输出进行系统分析更加现实。稳定性是网络物理系统安全性和鲁棒性最常见的要求之一。用于分析切换线性系统稳定性的现有方法通常需要了解底层系统的参数和/或所有状态。在本文中，我们提出了一种算法，用于纯粹基于观测到的输出数据来确定任意切换下切换线性系统的稳定性。所提出的算法本质上依赖于基于输出的李雅普诺夫稳定性框架，并返回联合谱半径（JSR）的估计。我们还从统计学习理论的角度证明了 JSR 估计质量的一个可能近似正确的误差界。