The Set of Linear Time-Invariant Unfalsified Models With Bounded Complexity is Affine

We consider exact system identification in the behavioral setting: Given an (noise-free) finite time series, find set of bounded complexity linear time-invariant systems that fit data exactly. First, we modify notion most powerful unfalsified model for case by fixing number inputs and minimizing order. Then, give necessary sufficient identifiability conditions, i.e., conditions under which true generating coincides with model. Finally, show models is affine: Every a sum autonomous complexity.