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Global Linearization of Parameterized Nonlinear Systems with Stable Equilibrium Point Using the Koopman Operator
Natsuki Katayama, Alexandre Mauroy, Yoshihiko Susuki
The Koopman operator framework enables global analysis of nonlinear systems through its inherent linearity. This study aims to clarify spectral properties of the Koopman operators…
Koopman Operators for Global Analysis of Hybrid Limit-Cycling Systems: Construction and Spectral Properties
Natsuki Katayama, Yoshihiko Susuki
This paper reports a theory of Koopman operators for a class of hybrid dynamical systems with globally asymptotically stable periodic orbits, called hybrid limit-cycling systems. W…
Participation Factors for Nonlinear Autonomous Dynamical Systems in the Koopman Operator Framework
Kenji Takamichi, Yoshihiko Susuki, Marcos Netto
We devise a novel formulation and propose the concept of modal participation factors to nonlinear dynamical systems. The original definition of modal participation factors (or simp…
Koopman Analysis of the Singularly-Perturbed van der Pol Oscillator
Natsuki Katayama, Yoshihiko Susuki
The Koopman operator framework holds promise for spectral analysis of nonlinear dynamical systems based on linear operators. Eigenvalues and eigenfunctions of the Koopman operator,…