We provide algorithmically verifiable necessary and sufficient conditions for fundamental system theoretic properties of discrete-time linear, systems subject to data losses. More precisely, the systems in our modeling framework are subject to disruptions (data losses) in the feedback loop, where the set of possible data loss sequences is captured by an automaton. As such, the results are applicable in the context of shared (wireless) communication networks and/or embedded architectures where some information on the data loss behavior is available a priori . We propose an algorithm for deciding observability (or the absence of it) for such systems, and show how this algorithm can be used also to decide other properties including constructibility, controllability, reachability, null-controllability, detectability, and stabilizability by means of relations that we establish among these properties. The main apparatus for our analysis is the celebrated Skolem's Theorem from Linear Algebra. Moreover, we study the relation between the model adopted in this paper and a previously introduced model where, instead of allowing dropouts in the feedback loop, one allows for time-varying delays.

中文翻译：

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遭受数据丢失的线性系统的可观测性和可控性分析


我们为离散时间线性系统的基本系统理论属性提供了可通过算法验证的必要和充分条件，系统会遭受数据丢失。更准确地说，我们的建模框架中的系统会受到反馈循环中的中断（数据丢失）的影响，其中一组可能的数据丢失序列由自动机捕获。因此，结果适用于共享（无线）通信网络和/或嵌入式架构的环境中，其中关于数据丢失行为的一些信息是先验可用的。我们提出了一种用于确定此类系统的可观测性（或不存在可观测性）的算法，并展示了如何使用该算法来通过关系来确定其他属性，包括可构造性、可控性、可达性、空可控性、可检测性和稳定性我们在这些属性中建立的。我们分析的主要工具是著名的线性代数斯科伦定理。此外，我们研究了本文采用的模型与之前引入的模型之间的关系，其中允许时变延迟，而不是允许反馈循环中的丢失。