The Singular Angle of Nonlinear Systems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866912472307335168 |
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| author | Chen, Chao Zhao, Di Khong, Sei Zhen |
| author_facet | Chen, Chao Zhao, Di Khong, Sei Zhen |
| contents | In this paper, we introduce an angle notion called the singular angle for nonlinear systems from an input-output perspective. The proposed system singular angle, based on the angle between $L_2$-signals, describes an upper bound for the ''rotating effect'' from system input to output signals. It quantifies passivity and serves as a counterpart to system $L_2$-gain. It also provides an alternative to a recently defined notion of system phase which adopts complexification of real-valued signals via the Hilbert transform. A nonlinear small angle theorem is established for feedback stability analysis, which involves a comparison of the loop system angle with $π$. The theorem generalizes the classical passivity theorem via a tradeoff between the singular angles of open-loop systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2109_01629 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The Singular Angle of Nonlinear Systems Chen, Chao Zhao, Di Khong, Sei Zhen Systems and Control Optimization and Control In this paper, we introduce an angle notion called the singular angle for nonlinear systems from an input-output perspective. The proposed system singular angle, based on the angle between $L_2$-signals, describes an upper bound for the ''rotating effect'' from system input to output signals. It quantifies passivity and serves as a counterpart to system $L_2$-gain. It also provides an alternative to a recently defined notion of system phase which adopts complexification of real-valued signals via the Hilbert transform. A nonlinear small angle theorem is established for feedback stability analysis, which involves a comparison of the loop system angle with $π$. The theorem generalizes the classical passivity theorem via a tradeoff between the singular angles of open-loop systems. |
| title | The Singular Angle of Nonlinear Systems |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2109.01629 |