Transactions of the Society of Instrument and Control Engineers
Online ISSN : 1883-8189
Print ISSN : 0453-4654
ISSN-L : 0453-4654
Category Theoretic Realization Theory of Basic Linear Syetems
Yasuhiko TAKAHARA
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1979 Volume 15 Issue 4 Pages 436-442

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Abstract
This paper is concerned with a category theoretic treatment of the realization theory of a basic linear system. In order to make a categorical problem of the realization we introduced two categories, the category of basic linear functional systems BLFS and that of basic linear dynamical systems BLDS, in addition to the category of basic linear systems BLS defined in another paper. The BLFS corresponds to a class of so-called“experiments”and is formulated as a category by extracting conditions when an experiment can be modeled into a basic linear system. The BLDS corresponds to a class of state space representations of basic linear systems and, similarly, their essential properties are extracted to be formulated as a category. Based on these categories, it was shown that two functors, a realization functor F1: BLFS→BLS and a representation functor F2: BLS→BLDS exist. It was also shown that F1 and F2 yield a universal and a co-universal map with respect to their corresponding forgetful functors G1: BLS→BLFS and G2: BLDS→BLS, respectively and that those maps correspond to categorical representations of controllability and observability. Finally, a category theoretic meaning of a minimum realization of a basic linear system is discussed.
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