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The Problem of Generalized D-Stability in Unbounded LMI Regions and Its Computational Aspects

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Abstract

We generalize the concepts of D-stability and additive D-stability of matrices. For this, we consider a family of unbounded regions defined in terms of Linear Matrix Inequalities (so-called LMI regions). We study the problem when the localization of a matrix spectrum in an unbounded LMI region is preserved under specific multiplicative and additive perturbations of the initial matrix. The most well-known particular cases of unbounded LMI regions (namely, conic sectors and shifted halfplanes) are considered. A new D-stability criterion as well as sufficient conditions for generalized D-stability are analyzed. Several applications of the developed theory to dynamical systems are shown.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shangda Road 99, 200444, Shanghai, China

    Olga Y. Kushel

  2. Department of Mathematics, Politecnico di Milano, Piazza L. da Vinci 32, 20133, Milano, Italia

    Raffaella Pavani

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  1. Olga Y. Kushel
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  2. Raffaella Pavani
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Correspondence to Raffaella Pavani.

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Kushel, O.Y., Pavani, R. The Problem of Generalized D-Stability in Unbounded LMI Regions and Its Computational Aspects. J Dyn Diff Equat 34, 651–669 (2022). https://doi.org/10.1007/s10884-020-09891-y

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  • DOI: https://doi.org/10.1007/s10884-020-09891-y

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