A STATIONARIZATION FUNCTOR AND ITS CONCRETE REALIZATIONS
Yasuhiko Takahara, Bumpei Nakano, Hiroshi KUBOTA · International Journal of General Systems · 1983
The purpose of this paper is lo investigate a transformation of systems in a category theoretic way and to reveal its structural property by showing that the famous Nerode realization and a well known stationarization operation are concrete realizations of the transformation. There is a well-known stationarization operation which transforms a lime variant tlynamicul model given by ż =ƒ(t,z,.x) and y = g(t,z,) into a time invariant dynamical model ([udot],ż)= (l.ƒ(u,z,x)) and y=g(u,z) where x, y and z are, respectively, an input, an output and a state variable. The paper integrates the Nerode realization and the above stationarization operation by one transformation and shows that they yield minimal causal stationary models using the category-theoretic treatment of the transformation. The paper demonstrates that the category theoretic consideration is powerful in integrating diversified systems concepts and in disclosing their underlying structures. In particular, a certain structural property of a stationary model will be clarified.