抄録
The realization problem of almost-linear systems had been presented with the following realization theorem. Realization theorem [For any invariant & affine input-response map (equivalently, any input/output map with causality, time-invariance and affinity), there exist at least two canonical almost-linear systems which realize it. Moreover any two canonical almost-linear systems with the same behavior are isomorphic each other.] And ‘so-call’ linear systems are examples of almost-linear systems. Moreover, the finite-dimensionality of the systems had been discussed.
In this paper, being based on the above results, we will discuss problems of the partial and real-time partial realization. The problems can be roughly described as the follows. The partial realization problem: [For a given partially time-invariant and affine input response map by multi-experiment, find a minimal dimensional almost linear system which partially realizes it.]
The real-time partially realization problem: [For a given partially time-invariant and affine input response map by single-experiment, find a minimal dimensional almost linear system which partially realizes it.]
And the following results are obtained.
(1) A necessary and sufficient condition for minimal partial realization systems to be unique is given by the rank condition of input/output matrix.
(2) For a given partially time-invariant and affine input response map by multi-experiment, an algorithm to obtain the minimal partial realization is given.
(3) For a given partially time-invariant and affine input response map by single experiment, an algorithm to obtain the minimal partial realization is given.
We conclude that these results about partial realization are the extension of the finite-dimensional, constant linear systems to almost linear systems which are non-linear systems.
