Characterizing matrices with eigenvalues in an LMI region: a dissipative-Hamiltonian approach
Neelam Choudhary, Nicolas Gillis, Punit Sharma · Linear and Multilinear Algebra · 2024
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∈Rn×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.