Reachable and observable sets for switched systems via generalized Lyapunov equations: application to switched descriptor systems
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910545702027264 |
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| author | Manucci, Mattia Unger, Benjamin |
| author_facet | Manucci, Mattia Unger, Benjamin |
| contents | In a recent work [Manucci, Unger, ArXiv e-print 2404.10511, 2024], the authors propose using two generalized Lyapunov equations (GLEs) to derive a balancing-based model order reduction~(MOR) method for a general class of switched differential-algebraic equations (DAEs). This work explains why these GLEs provide solutions suitable for MOR by showing that the image set of the solutions of the two GLEs always encloses the reachable and observable set of a suitably defined switched system with the same input to output map of the switched DAE system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20044 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reachable and observable sets for switched systems via generalized Lyapunov equations: application to switched descriptor systems Manucci, Mattia Unger, Benjamin Numerical Analysis Dynamical Systems 65P99, 93A30, 93B99 In a recent work [Manucci, Unger, ArXiv e-print 2404.10511, 2024], the authors propose using two generalized Lyapunov equations (GLEs) to derive a balancing-based model order reduction~(MOR) method for a general class of switched differential-algebraic equations (DAEs). This work explains why these GLEs provide solutions suitable for MOR by showing that the image set of the solutions of the two GLEs always encloses the reachable and observable set of a suitably defined switched system with the same input to output map of the switched DAE system. |
| title | Reachable and observable sets for switched systems via generalized Lyapunov equations: application to switched descriptor systems |
| topic | Numerical Analysis Dynamical Systems 65P99, 93A30, 93B99 |
| url | https://arxiv.org/abs/2407.20044 |