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Multidimensional Systems and Signal Processing

, Volume 20, Issue 4, pp 311–331 | Cite as

Strong practical stability and stabilization of discrete linear repetitive processes

  • Paweł Dąbkowski
  • Krzysztof Gałkowski
  • Eric Rogers
  • Anton Kummert
Article

Abstract

This paper considers two-dimensional (2D) discrete linear systems recursive over the upper right quadrant described by well known state-space models. Included are discrete linear repetitive processes that evolve over subset of this quadrant. A stability theory exists for these processes based on a bounded-input bounded-output approach and there has also been work on the design of stabilizing control laws, elements of which have led to the assertion that this stability theory is too strong in many cases of applications interest. This paper develops so-called strong practical stability as an alternative in such cases. The analysis includes computationally efficient tests that lead directly to the design of stabilizing control laws, including the case when there is uncertainty associated with the process model. The results are illustrated by application to a linear model approximation of the dynamics of a metal rolling process.

Keywords

2D information propagation Recursive updating Stability Stabilization 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Paweł Dąbkowski
    • 1
  • Krzysztof Gałkowski
    • 1
  • Eric Rogers
    • 2
  • Anton Kummert
    • 3
  1. 1.Institute of PhysicsNicolaus Copernicus University in TorunTorunPoland
  2. 2.School of Electronics and Computer ScienceUniversity of SouthamptonSouthamptonUK
  3. 3.Faculty of Electrical, Information and Media EngineeringUniversity of WuppertalWuppertalGermany

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