Causal and Stable Input/Output Structures on Multidimensional Behaviours

In this work we study multidimensional (nD) linear differential behaviours with a distinguished independent variable, called "time". We define in a natural way causality and stability of input/output structures with respect to this distinguished direction. We make an extension of some results in the theory of partial differential equations, demonstrating that causality is equivalent to a property of the transfer matrix. We also quote results which in effect characterize time-autonomy for the general systems case. Stability is likewise characterized by a property of the transfer matrix.