Characterizing matrices with eigenvalues in an LMI region: A dissipative-Hamiltonian approach
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866929666293497856 |
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| author | Choudhary, Neelam Gillis, Nicolas Sharma, Punit |
| author_facet | Choudhary, Neelam Gillis, Nicolas Sharma, Punit |
| contents | In this paper, we provide a dissipative Hamiltonian (DH) characterization for the set of matrices whose eigenvalues belong to a given LMI region. This characterization is a generalization of that of Choudhary et al. (Numer. Linear Algebra Appl., 2020) to any LMI region. It can be used in various contexts, which we illustrate on the nearest $Ω$-stable matrix problem: given an LMI region $Ω\subseteq \mathbb{C}$ and a matrix $A \in \mathbb{C}^{n,n}$, find the nearest matrix to $A$ whose eigenvalues belong to $Ω$. Finally, we generalize our characterization to more general regions that can be expressed using LMIs involving complex matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_07326 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Characterizing matrices with eigenvalues in an LMI region: A dissipative-Hamiltonian approach Choudhary, Neelam Gillis, Nicolas Sharma, Punit Optimization and Control Numerical Analysis In this paper, we provide a dissipative Hamiltonian (DH) characterization for the set of matrices whose eigenvalues belong to a given LMI region. This characterization is a generalization of that of Choudhary et al. (Numer. Linear Algebra Appl., 2020) to any LMI region. It can be used in various contexts, which we illustrate on the nearest $Ω$-stable matrix problem: given an LMI region $Ω\subseteq \mathbb{C}$ and a matrix $A \in \mathbb{C}^{n,n}$, find the nearest matrix to $A$ whose eigenvalues belong to $Ω$. Finally, we generalize our characterization to more general regions that can be expressed using LMIs involving complex matrices. |
| title | Characterizing matrices with eigenvalues in an LMI region: A dissipative-Hamiltonian approach |
| topic | Optimization and Control Numerical Analysis |
| url | https://arxiv.org/abs/2210.07326 |