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首页> 外文期刊>IEEE Transactions on Automatic Control >Interconnection and Memory in Linear Time-Invariant Systems
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Interconnection and Memory in Linear Time-Invariant Systems

机译：线性时不变系统中的互连和存储器

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摘要

We characterize the role played by memory when linear time-invariant systems interact. This study is of interest as the phenomenon that occurs in this setting is arguably the same phenomenon that governs some cascading failure and contagion effects in interconnected systems. We aim to later extend solutions presented in this paper to problems in other desired settings. The characterization relies on basic methods in homological algebra, and is reminiscent of the rank-nullity theorem of linear algebra. Interconnection of systems is first expressed as an exact sequence, then loss of memory causes a loss of exactness, and finally exactness is recovered through specific algebraic invariants of the systems that encode the role of memory. We thus introduce a new invariant, termed lag, of linear time-invariant systems and characterize the role of memory in terms of the lag. We discuss properties of the lag, and prove several results regarding the characterization.
机译：我们描述了线性时不变系统相互作用时记忆所起的作用。这项研究很有趣，因为在这种情况下发生的现象可以说是控制互连系统中某些级联故障和传染效应的同一现象。我们旨在稍后将本文介绍的解决方案扩展到其他所需设置中的问题。刻画依赖于同调代数中的基本方法，并且使人联想到线性代数的秩为零定理。系统的互连首先表示为精确的序列，然后记忆的丧失导致准确性的丧失，最后通过编码记忆作用的系统的特定代数不变量恢复准确性。因此，我们引入了线性时不变系统的新不变性，称为滞后，并根据滞后来表征记忆的作用。我们讨论了滞后的性质，并证明了有关表征的几个结果。

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