An SVD-like Decomposition of Bounded-Input Bounded-Output Functions
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913292369264640 |
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| author | Brown, Brian Charles King, Michael Warnick, Sean Yeung, Enoch Grimsman, David |
| author_facet | Brown, Brian Charles King, Michael Warnick, Sean Yeung, Enoch Grimsman, David |
| contents | The Singular Value Decomposition (SVD) of linear functions facilitates the calculation of their 2-induced norm and row and null spaces, hallmarks of linear control theory. In this work, we present a function representation that, similar to SVD, provides an upper bound on the 2-induced norm of bounded-input bounded-output functions, as well as facilitates the computation of generalizations of the notions of row and null spaces. Borrowing from the notion of "lifting" in Koopman operator theory, we construct a finite-dimensional lifting of inputs that relaxes the unitary property of the right-most matrix in traditional SVD, $V^*$, to be an injective, norm-preserving mapping to a slightly higher-dimensional space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00112 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An SVD-like Decomposition of Bounded-Input Bounded-Output Functions Brown, Brian Charles King, Michael Warnick, Sean Yeung, Enoch Grimsman, David Optimization and Control Systems and Control The Singular Value Decomposition (SVD) of linear functions facilitates the calculation of their 2-induced norm and row and null spaces, hallmarks of linear control theory. In this work, we present a function representation that, similar to SVD, provides an upper bound on the 2-induced norm of bounded-input bounded-output functions, as well as facilitates the computation of generalizations of the notions of row and null spaces. Borrowing from the notion of "lifting" in Koopman operator theory, we construct a finite-dimensional lifting of inputs that relaxes the unitary property of the right-most matrix in traditional SVD, $V^*$, to be an injective, norm-preserving mapping to a slightly higher-dimensional space. |
| title | An SVD-like Decomposition of Bounded-Input Bounded-Output Functions |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2404.00112 |