Duality bounds for discrete-time Zames-Falb multipliers
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866909135737454592 |
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| author | Zhang, Jingfan Carrasco, Joaquin Heath, William |
| author_facet | Zhang, Jingfan Carrasco, Joaquin Heath, William |
| contents | We develop phase limitations for the discrete-time Zames-Falb multipliers based on the separation theorem for Banach spaces. By contrast with their continuous-time counterparts they lead to numerically efficient results that can be computed either in closed form or via a linear program. The closed-form phase limitations are tight in the sense that we can construct multipliers that meet them with equality. We discuss numerical examples where the limitations are stronger than others in the literature. The numerical results complement searches for multipliers in the literature; they allow us to show, by construction, that the set of plants for which a suitable Zames-Falb multiplier exists is non-convex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_11975 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Duality bounds for discrete-time Zames-Falb multipliers Zhang, Jingfan Carrasco, Joaquin Heath, William Optimization and Control Systems and Control We develop phase limitations for the discrete-time Zames-Falb multipliers based on the separation theorem for Banach spaces. By contrast with their continuous-time counterparts they lead to numerically efficient results that can be computed either in closed form or via a linear program. The closed-form phase limitations are tight in the sense that we can construct multipliers that meet them with equality. We discuss numerical examples where the limitations are stronger than others in the literature. The numerical results complement searches for multipliers in the literature; they allow us to show, by construction, that the set of plants for which a suitable Zames-Falb multiplier exists is non-convex. |
| title | Duality bounds for discrete-time Zames-Falb multipliers |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2008.11975 |