Operator-Theoretic Characterization of Eventually Monotone Systems

Koopman operator; Monotone systems; Biological systems; Dynamical systems; Spectrum analyzers; Biologically inspired; Initial conditions; Partial order; Spectral characterization; Spectral properties; Vector fields; Linear systems

Abstract :

[en] Eventually monotone systems are dynamical systems whose solutions preserve a partial order in the initial condition after some initial transient. While monotone systems have a characterization in terms of their vector fields, eventually monotone systems have not been characterized in such an explicit manner. In order to provide a characterization, we drew inspiration from the results for linear systems, where eventually monotone (positive) systems are studied using the spectral properties of the system. We extend this spectral characterization to nonlinear systems by employing the Koopman operator framework. We also present a method to certify strong eventual monotonicity with respect to an unknown cone, a tool which to our best knowledge does not exist for monotone systems. These results are illustrated on biologically inspired numerical examples, which highlight the potential applicability of eventual monotonicity. © 2017 IEEE.

Disciplines :

Electrical & electronics engineering

Author, co-author :

Sootla, A.; Montefiore Institute, University of Liege, Liege, 4000, Belgium, Department of Engineering Science, University of Oxford, Oxford, OX1 3PJ, United Kingdom

Mauroy, Alexandre ; Université de Liège - ULiège

Language :

English

Title :

Operator-Theoretic Characterization of Eventually Monotone Systems

Publication date :

2018

Journal title :

IEEE Control Systems Letters

eISSN :

2475-1456

Volume :

Issue :

Pages :

429-434

Peer reviewed :

Peer reviewed

Available on ORBi :

since 18 December 2021

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