On the balanced truncation error bound and sign parameters from arrowhead realizations
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866929211155939328 |
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| author | Reiter, Sean Damm, Tobias Embree, Mark Gugercin, Serkan |
| author_facet | Reiter, Sean Damm, Tobias Embree, Mark Gugercin, Serkan |
| contents | Balanced truncation and singular perturbation approximation for linear dynamical systems yield reduced-order models that satisfy a well-known error bound involving the Hankel singular values. We show that this bound holds with equality for single-input, single-output systems, if the sign parameters corresponding to the truncated Hankel singular values are all equal. These signs are determined by a generalized state-space symmetry property of the corresponding linear model. For a special class of systems having arrowhead realizations, the signs can be determined directly from the off-diagonal entries of the corresponding arrowhead matrix. We describe how such arrowhead systems arise naturally in certain applications of network modeling, and illustrate these results with a power system model that motivated this study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_07170 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the balanced truncation error bound and sign parameters from arrowhead realizations Reiter, Sean Damm, Tobias Embree, Mark Gugercin, Serkan Systems and Control Dynamical Systems Optimization and Control 93B10, 93B11, 93C05 Balanced truncation and singular perturbation approximation for linear dynamical systems yield reduced-order models that satisfy a well-known error bound involving the Hankel singular values. We show that this bound holds with equality for single-input, single-output systems, if the sign parameters corresponding to the truncated Hankel singular values are all equal. These signs are determined by a generalized state-space symmetry property of the corresponding linear model. For a special class of systems having arrowhead realizations, the signs can be determined directly from the off-diagonal entries of the corresponding arrowhead matrix. We describe how such arrowhead systems arise naturally in certain applications of network modeling, and illustrate these results with a power system model that motivated this study. |
| title | On the balanced truncation error bound and sign parameters from arrowhead realizations |
| topic | Systems and Control Dynamical Systems Optimization and Control 93B10, 93B11, 93C05 |
| url | https://arxiv.org/abs/2011.07170 |