Recently a smooth compactification of the space of linear systems with $n$ states, $m$ inputs and $p$ outputs has been discovered. In this paper we obtain a concrete interpretation of this compactification as a space of discrete-time behaviors. We use both homogeneous polynomial representations and generalized first-order representations, and provide a realization theory to link these to each other.

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CWI
Department of Operations Research, Statistics, and System Theory [BS]

Ravi, M.S, Rosenthal, J, & Schumacher, J.M. (1996). Homogeneous behaviors. Department of Operations Research, Statistics, and System Theory [BS]. CWI.