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

10/13/2022

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by   Neelam Choudhary, et al.

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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⊆ℂ and a matrix A ∈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.