An Overview on Stability Theory in a Koopman Operator-Theoretic Perspective

Alexandre Mauroy ()
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Alexandre Mauroy: University of Namur and Namur Research Institute for Complex Systems (naXys)

Chapter 102 in Operator Theory, 2026, pp 3093-3117 from Springer

Abstract: Abstract This chapter presents a general overview of the Koopman operator-theoretic approach to stability analysis for dynamical systems. It describes the interplay between the convergence properties of a semiflow defined on a metric space and the stability properties of the associated semigroup of Koopman (or composition) operators. The main results focus on spectral properties, stability in reproducing kernel Hilbert spaces, and duality in stability theory.

Keywords: Stability; Dynamical system; Koopman operator; Composition operator; Lyapunov function; Reproducing kernel Hilbert space; Duality (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-16356-1_122

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DOI: 10.1007/978-3-032-16356-1_122

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