Algebraically Approximate and Noisy Realization of Linear Representation Systems

Abstract

Let the set of output’s values Y be a linear space over the field R. In the reference [Matsuo and Hasegawa, 2003], linear representation systems were presented with the following main theorem. The main theorem says that for any causal input/output map, i.e., any input response map, there exist at least two canonical, namely quasi-reachable and distinguishable linear representation systems which realize, equivalently, faithfully describe it, and any two canonical linear representation systems with the same behavior are isomorphic.