On the Computation of Stabilizing Controllers of Multidimensional Systems

In this paper, we consider the open problem consisting in the computation of stabilizing controllers of an internally stabilizable MIMO multidimensional system. Based on homological algebra and the so-called Polydisk Nullstellensatz, we propose a general method towards the explicit computation of stabilizing controllers. We show how homological algebra methods over the ring of structurally stable SISO multidimensional transfer functions can be made algorithmic based on standard Grobner basis techniques over polynomial rings. The problem of computing stabilizing controllers is then reduced to the problem of obtaining an effective version of the Polydisk Nullstellensatz which, apart from a few cases, stays open and will be studied in forthcoming publications. Copyright (C) 2019. The Authors. Published by Elsevier Ltd. All rights reserved.