Globally Exponential Stability Analysis: An Enhanced Approach via Koopman Operator Theory

This paper adapts Koopman operator for global stability analysis, which is a relatively novel method. Novel theoretical results for the special case of global exponential stability analysis are introduced and substantiated. Subsequently, to enhance the computation of Koopman eigenfunctions, a new methodology leveraging orthogonal basis functions is proposed, which demonstrates distinct advantages and efficacy compared with existing methods. The proposed method is validated through theoretical proofs and numerical experiments, ensuring its reliability and practical applicability.