On the representation of 2-D systems

The behavioral approach to 2-D systems essentially consists in viewing a system as a family of admissible signals (the system behavior) instead of as a set of describing equations (which constitute a system representation). From this stand point, it is natural to define properties of systems in terms of their signals and not of their representations. The translation of the system structure into properties of the representation parameters is, of course, a crucial issue, but in our opinion should not be taken as a starting point. This paper is mainly concerned with the study of controllability properties in the above framework. Our notions differ from the classical ones as they are introduced as properties of the external signals, without making appeal to state space realizations. Controllabilite of state space systems can however be considered as a particular case of our definitions if the state is regarded as an external variable.