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Regularity and Stability Sets for Families of Sequences of Matrices

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Abstract

We consider the notions of Lyapunov regularity and of Lyapunov stability and asymptotic stability for a dynamics defined by a continuous 1-parameter family of sequences of matrices. In particular, we identify all classes of sets that can be the regularity set, the stability set and the asymptotic stability set of any such family. Moreover, we construct explicitly families of sequences of matrices whose regularity set, stability set or asymptotic stability set is a given set in those classes.

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Authors and Affiliations

  1. Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001, Lisbon, Portugal

    Luis Barreira & Claudia Valls

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  1. Luis Barreira
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  2. Claudia Valls
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Correspondence to Luis Barreira.

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Partially supported by FCT/Portugal through the Project UID/MAT/04459/2013.

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Barreira, L., Valls, C. Regularity and Stability Sets for Families of Sequences of Matrices. J Dyn Diff Equat 32, 1603–1630 (2020). https://doi.org/10.1007/s10884-019-09795-6

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  • DOI: https://doi.org/10.1007/s10884-019-09795-6

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