Nonlinear left and right eigenvectors for max-preserving maps

Title: Nonlinear left and right eigenvectors for max-preserving maps
Creator: Rüffer, Björn S.
Relation: Positive Systems Theory and Applications (POSTA 2016). Positive Systems: Theory and Applications (POSTA 2016) Rome, Italy, September 14-16, 2016 [presnted in Lecture Notes in Control and Information Sciences, Vol. 471] (Rome, Italy 14-16 September, 2016) p. 227-237
Publisher Link: http://dx.doi.org/10.1007/978-3-319-54211-9_18
Publisher: Springer
Resource Type: conference paper
Date: 2017
Description: 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.
Subject: monotone systems; join-morphisms; Perron-Frobenius theory; positive eigenvectors; small-gain condition; Lyapunov functions
Identifier: http://hdl.handle.net/1959.13/1400786
Identifier: uon:34814
Identifier: ISBN:9783319542102
Language: eng
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