The behavioural approach to distributed systems

In the behavioural approach to systems theory, one describes behaviours as solutions of high order differential equations. This behaviour is then identified with the system, emphasising the fact that different sets of differential equations could still describe the same system whereas the behaviour is an invariant of the system. It is convenient to think of these systems of differential equations in terms of matrices over polynomial rings. It has been shown that certain algebraic objects (namely modules) can be uniquely identified with a given behaviour. System theoretic properties of a behaviour, like controllability and autonomy can then be shown as properties of this behaviour. In this paper, this behavioural approach to N-D systems is introduced, so that these concepts can then be made use of in our companion paper (see ibid.) which extends the theory of storage functions and dissipation to N-D systems. We also introduce the concept of observability. It is shown that only certain controllable N-D behaviours have an observable image representation