Stabilization of discrete 2D behaviors by regular partial interconnection

Abstract

In this work, we consider linear, shift-invariant and complete twodimensional (2D) discrete systems from a behavioral point of view. In particular, we examine behaviors with two types of variables: the variables that we are interested to control (the to-be-controlled variables) and the variables on which we are allowed to enforce restrictions (the control variables). The main purpose of this contribution is to derive necessary and sufficient conditions for the stabilization of the to-be-controlled variables by 'attaching' a controller to the control variables. This problem turns out to be related to the decomposition of a given behavior into the sum of two sub-behaviors. Moreover, we show that under certain conditions, it is possible to obtain a constructive solution and characterize the structure of the to-be-controlled behavior. Mathematics Subject Classification (2000)93B05 · 93B07 · 93B25 · 93C05 · 93C35 · 93C65 · 93D15

A Generalized Tracking and Disturbance Rejection Problem for Multidimensional Behaviors

“…Stimulated by two milestone contributions [20,21], dealing with the control of one-dimensional behaviours, a long stream of research on these topics flourished, dealing either with one-dimensional (1D) behaviours (e.g. [1,3,4,12]) or with the wider class of multidimensional (nD) behaviours [5,6,8,13,18].…”

“…ass(M) is the set of all prime ideals p such that there is a monomorphism from A/p to M 6. http://www.singular.uni-kl.de/…”