  The paper studies conical, convex, and affine models in the framework of
behavioral systems theory. We investigate basic properties of such behaviors
and address the problem of constructing models from measured data. We prove
that closed, shift-invariant, conical, convex, and affine models have the
intersection property, thereby enabling the definition of most powerful
unfalsified models based on infinite-horizon measurements. We then provide
necessary and sufficient conditions for representing conical, convex, and
affine finite-horizon behaviors using raw data matrices, expressing persistence
of excitation requirements in terms of non-negative rank conditions. The
applicability of our results is demonstrated by a numerical example arising in
population ecology.
