On Koopman Resolvents and Frequency Response of Nonlinear Systems
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | |
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| _version_ | 1866910106864582656 |
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| author | Susuki, Yoshihiko Katayama, Natsuki Mauroy, Alexandre Mezić, Igor |
| author_facet | Susuki, Yoshihiko Katayama, Natsuki Mauroy, Alexandre Mezić, Igor |
| contents | This paper proposes a novel formulation of frequency response for nonlinear systems in the Koopman operator framework. This framework is a promising direction for the analysis and synthesis of systems with nonlinear dynamics based on (linear) Koopman operators. We show that the frequency response of a nonlinear plant is derived through the Laplace transform of the output of the plant, which is a generalization of the classical approach to LTI plants and is guided by the resolvent theory of Koopman operators. The response is a complex-valued function of the driving angular frequency, allowing one to draw the so-called Bode plots, which display the gain and phase characteristics. Sufficient conditions for the existence of the frequency response are presented for three classes of dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05771 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Koopman Resolvents and Frequency Response of Nonlinear Systems Susuki, Yoshihiko Katayama, Natsuki Mauroy, Alexandre Mezić, Igor Systems and Control Dynamical Systems Optimization and Control This paper proposes a novel formulation of frequency response for nonlinear systems in the Koopman operator framework. This framework is a promising direction for the analysis and synthesis of systems with nonlinear dynamics based on (linear) Koopman operators. We show that the frequency response of a nonlinear plant is derived through the Laplace transform of the output of the plant, which is a generalization of the classical approach to LTI plants and is guided by the resolvent theory of Koopman operators. The response is a complex-valued function of the driving angular frequency, allowing one to draw the so-called Bode plots, which display the gain and phase characteristics. Sufficient conditions for the existence of the frequency response are presented for three classes of dynamics. |
| title | On Koopman Resolvents and Frequency Response of Nonlinear Systems |
| topic | Systems and Control Dynamical Systems Optimization and Control |
| url | https://arxiv.org/abs/2603.05771 |