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Stability of one-dimensioned spatially interconnected systems

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Abstract

This article is dedicated to the stability of one-dimensioned spatially interconnected systems. More precisely, it focuses on systems which results of the interconnection of a possibly large number of cells (continuous subsystems). This note is restricted to the case where cells are just distributed along a line. The global system can then be seen as a mixed continuous–discrete 2D Roesser system but with implicit discrete dynamics along the space dimension. Recent results on the stability of 2D Roesser models are exploited and adapted to derive a sufficient condition for such a system to be stable. The condition seems to be close to necessity if not necessary. It is tractable since it is expressed in terms of linear matrix inequalities. The novelty clearly lies in the reduction of the conservatism of the proposed analysis.

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Notes

  1. This commonly used term is actually not appropriate in the present article since this transform will be applied on a space dimension and the term “discrete-space Fourier transform” is probably more appropriate and it is used in the remainder of the article.

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Authors and Affiliations

  1. LIAS-ENSIP, University of Poitiers, Bâtiment B25, 2 Rue Pierre Brousse, TSA 41105, 86073, Poitiers Cedex 9, France

    Olivier Bachelier & Nima Yeganefar

  2. CNRS XLIM UMR 7252, University of Limoges, 123 Avenue Albert Thomas, 87060, Limoges Cedex, France

    Thomas Cluzeau & Francisco José Silva Alvarez

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  1. Olivier Bachelier
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  2. Thomas Cluzeau
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  3. Francisco José Silva Alvarez
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  4. Nima Yeganefar
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Correspondence to Olivier Bachelier.

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Bachelier, O., Cluzeau, T., Silva Alvarez, F.J. et al. Stability of one-dimensioned spatially interconnected systems. Multidim Syst Sign Process 31, 1005–1028 (2020). https://doi.org/10.1007/s11045-019-00695-y

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