2024-03-28T09:47:37Z
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oai:nagoya.repo.nii.ac.jp:00005264
2023-01-16T03:49:52Z
320:321:322
What are singular values of nonlinear operators?
Fujimoto, Kenji
13315
This paper is devoted to a novel characterization of singular values of nonlinear operators. Although eigenvalue and spectrum analysis for nonlinear operators has been studied by many researchers in mathematics literature, singular value analysis has not been investigated so much. In this paper, a novel framework of singular value analysis is proposed which is closely related to the operator gain. The proposed singular value analysis is based on the eigenvalue analysis of a special class of nonlinear operators called differentially self-adjoint. Some properties of those operators are clarified which are natural generalization of the linear case results. Furthermore, a sufficient condition for the existence of singular values is provided. The proposed analysis tools are expected to play an important role in nonlinear control systems theory as in the linear case.
journal article
IEEE
2004-12
application/pdf
43rd IEEE Conference on Decision and Control 2004
2
2
1623
1628
http://hdl.handle.net/2237/6851
https://nagoya.repo.nii.ac.jp/record/5264/files/cdc04.pdf
eng
https://doi.org/10.1109/CDC.2004.1430277
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