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Nonlinear Left and Right Eigenvectors for Max-Preserving Maps

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Positive Systems (POSTA 2016)

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 471))

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Abstract

It is shown that max-preserving maps (or join-morphisms) on the positive orthant in Euclidean n-space endowed with the component-wise partial order give rise to a semiring. This semiring admits a closure operation for maps that generate stable dynamical systems. For these monotone maps, the closure is used to define suitable notions of left and right eigenvectors that are characterized by inequalities. Some explicit examples are given and applications in the construction of Lyapunov functions are described.

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Authors and Affiliations

  1. School of Mathematical and Physical Sciences, The University of Newcastle (UON), Callaghan, NSW, 2308, Australia

    Björn S. Rüffer

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  1. Björn S. Rüffer
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Correspondence to Björn S. Rüffer .

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Editors and Affiliations

  1. Università Campus Biomedico , Rome, Italy

    Filippo Cacace

  2. Sapienza Università di Roma , Rome, Italy

    Lorenzo Farina

  3. Università Campus Biomedico , Rome, Italy

    Roberto Setola

  4. Università dell’Aquila , L'Aquila, Italy

    Alfredo Germani

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Rüffer, B.S. (2017). Nonlinear Left and Right Eigenvectors for Max-Preserving Maps. In: Cacace, F., Farina, L., Setola, R., Germani, A. (eds) Positive Systems . POSTA 2016. Lecture Notes in Control and Information Sciences, vol 471. Springer, Cham. https://doi.org/10.1007/978-3-319-54211-9_18

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  • DOI: https://doi.org/10.1007/978-3-319-54211-9_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-54210-2

  • Online ISBN: 978-3-319-54211-9

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