Equivalence and Reduction of Repetitive Discrete Linear Systems

Over the last four decades, there has been a growing interest in the area of two-dimensional systems theory. This is motivated by the wide variety of applications e.g. 2-D circuits and signal processing, and repetitive linear systems to mention but a few. A 2D linear system is a system in which information propagates in two independent directions. Linear repetitive systems are one of the most important class of 2-D systems from the practical point of view. Such systems are characterized by a series of sweeps or passes with the requirement that a specified output trajectory over a finite interval is followed to a high precision. Linear repetitive processes turn out to be very similar to the so called 2D Roesser state-space models. In this project we intend to apply Galkowski s Elementary Operations Algorithm (EOA) to obtain equivalent system representations and to investigate the exact connection linking the original system to the reduced one.