RATIONAL REPRESENTATIONS OF BEHAVIORS - INTERCONNECTABILITY AND STABILIZABILITY

This paper presents an analysis of representation and stability proper ties of dynamical systems whose signals are assumed to be square summa ble sequences. Systems are defined as families of trajectories with no more structure than linearity and shift invariance. We depart from th e usual input-output and operator theoretic setting and view relations hips among system variables as a more general starting point for the s tudy of dynamical systems. Parametrizations of two model classes are d erived in terms of analytic functions which define kernel and image re presentations of dynamical systems. It is shown how state space models are derived from these representations. Uniqueness and minimality of these representations are completely characterized. Elementary propert ies like stabilizability, regularity, and interconnectability of dynam ical systems are introduced and characterized in this set theoretic fr amework.