Time-relevant 2D behaviors

In this work we present some results on 2D behaviors described by linear constant coefficient partial difference equations where one of the independent variables, “time”, is distinguished and plays a special role. We call such systems `time-relevant'. We first give a test to check time-relevance starting from an arbitrary description of the behavior. Then, we introduce a stability notion for these systems and provide an algebraic test in terms of the location of the zeros of the determinant of a polynomial matrix describing the system.