On the Computation of Stabilizing Controllers of Multidimensional Systems

被引：1

作者：

Bouzidi, Y. ^{[1
]}

Cluzeau, T. ^{[2
,3
]}

Quadrat, A. ^{[4
]}

机构：

[1] Inria Lille, Lille, France

[2] CNRS, F-87060 Limoges, France

[3] XLIM UMR 7252, F-87060 Limoges, France

[4] Sorbonne Univ, Inria Paris, Ouragan Project Team, IMJ PRG, Paris, France

来源：

IFAC PAPERSONLINE | 2019年 / 52卷 / 17期

关键词：

Fractional representation approach; internal stabilization; stabilizing controllers; multidimensional systems; infinite-dimensional systems; computer algebra; FRACTIONAL REPRESENTATION APPROACH; ALGEBRAIC ANALYSIS VIEWPOINT; LATTICE APPROACH; PART II;

D O I：

10.1016/j.ifacol.2019.11.032

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页码：88 / 93

页数：6

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