Least order conditions for a 2-D system in Roesser form

The concepts of observability, controllability and minimality form the foundation for many design and synthesis techniques in classical single variable system theory. Rosenbrock (1968) provides dual sets of necessary and sufficient conditions for a system in state space form to be observable or controllable. A system which is controllable and observable, may be shown to be minimal. A number of practical problems (coal mining operations, metal rolling, etc.) have focused attention on systems which are modelled using two independent variables (2D systems). A number of such models offer first-order state-space-like forms. A particularly general first order form is the Roesser form (1975) and it is with this, and the way in which Rosenbrock´s results can be generalised for if that the paper will be concerned