離散時間・擬線形系の実現理論

抄録

In this paper the discrete-time system is treated. And it is discussed the realization problem of pseudo-linear systems to be the special class of affaine dynamical systems. Pseudo-linear systems are the affaine dynamical systems in which free motions are able to be considered. The realization theorem of affaine dynamical systems had already been established. The theorem being based on, realization problem of pseudo-linear systems is discussed.
Generally speaking, the realization problem is stated as follows.
[Let I/O be the set of input/output map to be a black-box and CD be the category of dynamical systems which have the same behavior as the given black-box, it is intended to obtain the following realization theorem.
Realization theorem:⌈For any given input/output map a∈I/O, there exist at least one dynamical system σ∈CD which has the behavior a. Let any σ₁, σ₂∈CD have the same behavior, then σ₁ is isomorphic to σ₂ in sense of category CD.⌋]
In the realization problem of affine dynamical systems, let I/O be the set of any input/output map with causality (that is equal to treating any input-response map), let CD be the category of canonical (quasi-reachable and distingushable) affine dynamical systems, then the realization theorem of affine dynamical systems have been obtained.
In this paper, let I/O be the set of any input-response map with time-invariance and let CD be the category of pseudo-linear systems, then the realization theorem of pseudo-linear systems is obtained.
It is also showed that electric circuits with a transistor are examples of pseudo-linear systems.