Linear Dynamical Systems over Finite Rings

Q3 Engineering

IFAC-PapersOnLine Pub Date : 2024-01-01 DOI:10.1016/j.ifacol.2024.10.198

Yannic Rohde , Eva Zerz

引用次数: 0

Abstract

We present the theory of linear systems over various kinds of finite commutative rings. Since these systems are finite, the trajectories have to run into repeating cycles eventually. This periodic behavior is the main interest of this topic. Using an approach similar to Fitting's lemma, a bijective-nilpotent decomposition of the system can be achieved, which in some cases even gives a decomposition of the system matrix. In particular, this allows us, to apply results about invertible system matrices, where all trajectories are purely periodic, to the more general setting. Finally, the algorithmic potential of the theory is discussed.

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有限环上的线性动力系统

我们介绍了各种有限交换环上的线性系统理论。由于这些系统都是有限的，其轨迹最终都会进入重复周期。这种周期行为是本课题的主要兴趣所在。利用类似于菲廷 Lemma 的方法，可以得到系统的双射-无势分解，在某些情况下甚至可以得到系统矩阵的分解。特别是，这使我们能够将所有轨迹都是纯周期性的可逆系统矩阵的结果应用到更一般的环境中。最后，我们将讨论该理论在算法方面的潜力。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IFAC-PapersOnLine Engineering-Control and Systems Engineering

CiteScore

1.70

自引率

0.00%

发文量

1122

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