Global Linearization of Parameterized Nonlinear Systems with Stable Equilibrium Point Using the Koopman Operator
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911569572528128 |
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| author | Katayama, Natsuki Mauroy, Alexandre Susuki, Yoshihiko |
| author_facet | Katayama, Natsuki Mauroy, Alexandre Susuki, Yoshihiko |
| contents | 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 for nonlinear systems with control inputs. To this end, we treat the inputs as parameters throughout this paper. We then introduce the Koopman operator for a parameterized dynamical system with a globally exponentially stable equilibrium point and analyze how eigenfunctions of the operator depend on the parameter. As a main result, we obtain a global linearization, which enables one to transform the nonlinear system into a finite-dimensional linear system, and we show that it depends continuously on the parameter. Subsequently, for a control-affine system, we investigate a condition under which the transformation providing a global bilinearization does not depend on the parameter. This provides the condition under which the global bilinearization for the control-affine system is independent of the parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04711 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global Linearization of Parameterized Nonlinear Systems with Stable Equilibrium Point Using the Koopman Operator Katayama, Natsuki Mauroy, Alexandre Susuki, Yoshihiko Dynamical Systems Systems and Control 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 for nonlinear systems with control inputs. To this end, we treat the inputs as parameters throughout this paper. We then introduce the Koopman operator for a parameterized dynamical system with a globally exponentially stable equilibrium point and analyze how eigenfunctions of the operator depend on the parameter. As a main result, we obtain a global linearization, which enables one to transform the nonlinear system into a finite-dimensional linear system, and we show that it depends continuously on the parameter. Subsequently, for a control-affine system, we investigate a condition under which the transformation providing a global bilinearization does not depend on the parameter. This provides the condition under which the global bilinearization for the control-affine system is independent of the parameter. |
| title | Global Linearization of Parameterized Nonlinear Systems with Stable Equilibrium Point Using the Koopman Operator |
| topic | Dynamical Systems Systems and Control |
| url | https://arxiv.org/abs/2604.04711 |