Strong practical stability and stabilization of uncertain discrete linear repetitive processes

Authors

  • Pawel Dabkowski,

    Corresponding author
    1. Institute of Physiscs, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Torun, Poland
    • Institute of Information Theory and Automation, Czech Academy of Sciences, Prague 8, Czech Republic
    Search for more papers by this author
  • Krzysztof Galkowski,

    1. Institute of Physiscs, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Torun, Poland
    2. Faculty of Electrical, Information and Media Engineering, Communication Theory University of Wuppertal, Germany as a Gerhard Mercator Guest Professor (DFG)
    Search for more papers by this author
  • Olivier Bachelier,

    1. LAII, ESIP, University of Poitiers, France
    Search for more papers by this author
  • Eric Rogers,

    1. School of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ
    Search for more papers by this author
  • Anton Kummert,

    1. Faculty of Electrical, Information and Media Engineering, Communication Theory University of Wuppertal, Germany
    Search for more papers by this author
  • James Lam

    1. Department of Mechanical Engineering, University of Hong Kong
    Search for more papers by this author

  • This work was supported by Ministry of Education of the Czech Republic within project Center for Applied Cybernetics No. 1M0567

Correspondence to: Pawel Dabkowski, Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Torun, Poland.

E-mail: p.dabkowski@fizyka.umk.pl

SUMMARY

Repetitive processes are a distinct class of 2D systems of both theoretical and practical interest. The stability theory for these processes originally consisted of two distinct concepts termed asymptotic stability and stability along the pass, respectively, where the former is a necessary condition for the latter. Recently applications have arisen where asymptotic stability is too weak, and stability along the pass is too strong for meaningful progress to be made. This, in turn, has led to the concept of strong practical stability for such cases, where previous work has formulated this property and obtained necessary and sufficient conditions for its existence together with Linear Matrix Inequality based tests, which then extend to allow robust control law design. This paper develops considerably simpler, and hence computationally more efficient, stability tests that also extend to allow control law design. Copyright © 2011 John Wiley & Sons, Ltd.

Ancillary