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Mathematics > Optimization and Control

arXiv:2210.07326 (math)
[Submitted on 13 Oct 2022]

Title:Characterizing matrices with eigenvalues in an LMI region: A dissipative-Hamiltonian approach

Authors:Neelam Choudhary, Nicolas Gillis, Punit Sharma
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Abstract: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 $\Omega$-stable matrix problem: given an LMI region $\Omega \subseteq \mathbb{C}$ and a matrix $A \in \mathbb{C}^{n,n}$, find the nearest matrix to $A$ whose eigenvalues belong to $\Omega$. Finally, we generalize our characterization to more general regions that can be expressed using LMIs involving complex matrices.
Comments: 15 pages, 2 figures
Subjects: Optimization and Control (math.OC); Numerical Analysis (math.NA)
Cite as: arXiv:2210.07326 [math.OC]
  (or arXiv:2210.07326v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2210.07326

Submission history

From: Nicolas Gillis [view email]
[v1] Thu, 13 Oct 2022 19:53:23 UTC (165 KB)
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