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New tests for the stability of 3D Roesser models

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Abstract

This article provides new conditions for testing the structural stability of 3D Roesser models. The models can be discrete, continuous, or mixed discrete/continuous. The conditions consist in a few tests on the eigenvalues of matrices and one test on an auxiliary 2D model. The latter test is based upon a hierarchy of linear matrix inequalities relaxations. The global test for structural stability is necessary and sufficient for a large enough value of the hierarchy level.

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Acknowledgements

The authors would like to thank the anonymous reviewers of the first version of this paper for their careful reading and relevant comments which have improved both the readability and the clarity of the paper.

Funding

This work is supported by the MIRES (Mathematiques et leurs Interactions, Images et information numerique, Reseaux et Seurite) research federation.

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Authors and Affiliations

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

    Olivier Bachelier, Driss Mehdi, Alexandre Rigaud & Nima Yeganefar

  2. CNRS, XLIM, UMR 7252, University of Limoges, 87000, Limoges, France

    Thomas Cluzeau

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  1. Olivier Bachelier
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  2. Thomas Cluzeau
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  4. Alexandre Rigaud
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  5. Nima Yeganefar
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All the authors took part in the writing of the article.

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Correspondence to Olivier Bachelier.

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Bachelier, O., Cluzeau, T., Mehdi, D. et al. New tests for the stability of 3D Roesser models. Math. Control Signals Syst. 35, 619–639 (2023). https://doi.org/10.1007/s00498-023-00352-7

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  • DOI: https://doi.org/10.1007/s00498-023-00352-7

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