Abstract
The realization problem of linear representation systems had been presented with the following realization theorem. Realization theorem [For any input response map (equivalently, any input/output map with causality), there exist at least two canonical linear representation systems which realize it. Moreover, Any two canonical linear representation systems with the same behavior are isomorphic.]
And the finite dimensional of the systems had been also discussed. Moreover, for a data obtained by multi-experiment, the partial realization problem of the systems had been discussed. Where any non-linear systems with on-off control, any homogeneous bilinear systems and any K-Σ-automata are examples of linear representation systems.
In this paper, being based on the above results, we will discuss a problem of the real-time partial realization. The problem can be roughly described as the follows.
[For a given partial input response map by single experiment, find uniquely a minimal dimensional linear representation system which realizes it.]
Introducing invertible linear representation systems, we will obtain the real-time partial realization theorem.
In the field of automata, the identification problem of automata have been solved with introducing the notion of “strongly connected”, which is weaker than the notion “invertible”. Namely, “strongly connected” implies “invertible” and the converse does not hold.
We conclude that the result of this paper is the extension of the finite dimensional, constant, linear systems to a non-linear systems.
