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Positive Systems pp 207–214Cite as

Stability of Linear Systems and Positive Semigroups of Symmetric Matrices

  • Invited Session: Positivity and Stability
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Control and Information Science ((LNCIS,volume 294))

Abstract

The role of Lyapunov operators in stability theory is well-known. In this paper we present an interesting characterization of Lyapunov operators. We show that an operator generates a positive group on the real space of real or complex Hermitian matrices, if and only if it is a Lyapunov operator.

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Authors and Affiliations

  1. Institute of Applied Mathematics, TU Braunschweig, Germany

    Tobias Damm

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  1. Tobias Damm
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Luca Benvenuti Alberto De Santis Lorenzo Farina

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Cite this paper

Damm, T. Stability of Linear Systems and Positive Semigroups of Symmetric Matrices. In: Benvenuti, L., De Santis, A., Farina, L. (eds) Positive Systems. Lecture Notes in Control and Information Science, vol 294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44928-7_28

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  • DOI: https://doi.org/10.1007/978-3-540-44928-7_28

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40342-5

  • Online ISBN: 978-3-540-44928-7

  • eBook Packages: Springer Book Archive

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