Bilinear Quadratic Output Systems and Balanced Truncation
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909675869437952 |
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| author | Faßbender, Heike Gugercin, Serkan Peters, Till |
| author_facet | Faßbender, Heike Gugercin, Serkan Peters, Till |
| contents | Dynamical systems with quadratic outputs have recently attracted significant attention. In this paper, we consider bilinear dynamical systems, a special class of weakly nonlinear systems, with a quadratic output. We develop various primal-dual formulations for these systems and define the corresponding system Gramians. Conditions for the existence and uniqueness of these Gramians are established, and the generalized Lyapunov equations they satisfy are derived. Using these Gramians and their truncated versions, which are computationally more efficient, we construct a balanced truncation framework for bilinear systems with quadratic outputs. The proposed approach is demonstrated through two numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03684 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bilinear Quadratic Output Systems and Balanced Truncation Faßbender, Heike Gugercin, Serkan Peters, Till Numerical Analysis 93A15, 93B05, 93B07, 93C10, 93C15 Dynamical systems with quadratic outputs have recently attracted significant attention. In this paper, we consider bilinear dynamical systems, a special class of weakly nonlinear systems, with a quadratic output. We develop various primal-dual formulations for these systems and define the corresponding system Gramians. Conditions for the existence and uniqueness of these Gramians are established, and the generalized Lyapunov equations they satisfy are derived. Using these Gramians and their truncated versions, which are computationally more efficient, we construct a balanced truncation framework for bilinear systems with quadratic outputs. The proposed approach is demonstrated through two numerical examples. |
| title | Bilinear Quadratic Output Systems and Balanced Truncation |
| topic | Numerical Analysis 93A15, 93B05, 93B07, 93C10, 93C15 |
| url | https://arxiv.org/abs/2507.03684 |