Affordable Access

Access to the full text

On the stability and the stabilization of linear discrete repetitive processes

Authors
  • Bachelier, Olivier1
  • Cluzeau, Thomas2
  • Yeganefar, Nima1
  • 1 University of Poitiers, LIAS-ENSIP, Bâtiment B25, 2 rue Pierre Brousse, TSA 41105, Poitiers Cedex 9, 86073, France , Poitiers Cedex 9 (France)
  • 2 University of Limoges, CNRS XLIM UMR 7252, 123 avenue Albert Thomas, Limoges cedex, 87060, France , Limoges cedex (France)
Type
Published Article
Journal
Multidimensional Systems and Signal Processing
Publisher
Springer US
Publication Date
May 26, 2018
Volume
30
Issue
2
Pages
963–987
Identifiers
DOI: 10.1007/s11045-018-0583-3
Source
Springer Nature
Keywords
License
Yellow

Abstract

This article deals with stability and stabilization issues for linear two-dimensional (2D) discrete models. More precisely, we focus on repetitive processes and Roesser models. Within the algebraic analysis approach to linear systems theory, we first show how a given linear repetitive process can be transformed into an equivalent linear Roesser model. We then prove that the structural stability is preserved by this equivalence transformation. This enables us to design new approaches for stabilizing linear repetitive processes by means of existing methods for computing a state feedback control law stabilizing a linear 2D discrete Roesser model. We also show that we can interpret the stability along the pass of a linear repetitive process as its structural stability. This implies that one of our new approaches can be applied to stabilize along the pass a linear repetitive process which is only stable from pass to pass.

Report this publication

Statistics

Seen <100 times