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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.

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

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  • 发表日期：

    2026年

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  • A. Mauroy

摘要

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.