On approximating the nearest Ω-stable matrix
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2019
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| _version_ | 1866912161479000064 |
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| author | Choudhary, Neelam Gillis, Nicolas Sharma, Punit |
| author_facet | Choudhary, Neelam Gillis, Nicolas Sharma, Punit |
| contents | In this paper, we consider the problem of approximating a given matrix with a matrix whose eigenvalues lie in some specific region Ω, within the complex plane. More precisely, we consider three types of regions and their intersections: conic sectors, vertical strips and disks. We refer to this problem as the nearest Ω-stable matrix problem. This includes as special cases the stable matrices for continuous and discrete time linear time-invariant systems. In order to achieve this goal, we parametrize this problem using dissipative Hamiltonian matrices and linear matrix inequalities. This leads to a reformulation of the problem with a convex feasible set. By applying a block coordinate descent method on this reformulation, we are able to compute solutions to the approximation problem, which is illustrated on some examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_03069 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | On approximating the nearest Ω-stable matrix Choudhary, Neelam Gillis, Nicolas Sharma, Punit Optimization and Control Numerical Analysis In this paper, we consider the problem of approximating a given matrix with a matrix whose eigenvalues lie in some specific region Ω, within the complex plane. More precisely, we consider three types of regions and their intersections: conic sectors, vertical strips and disks. We refer to this problem as the nearest Ω-stable matrix problem. This includes as special cases the stable matrices for continuous and discrete time linear time-invariant systems. In order to achieve this goal, we parametrize this problem using dissipative Hamiltonian matrices and linear matrix inequalities. This leads to a reformulation of the problem with a convex feasible set. By applying a block coordinate descent method on this reformulation, we are able to compute solutions to the approximation problem, which is illustrated on some examples. |
| title | On approximating the nearest Ω-stable matrix |
| topic | Optimization and Control Numerical Analysis |
| url | https://arxiv.org/abs/1901.03069 |