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

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 $ \Omega \subseteq {\mathbb C} $ Ω ⊆ C and a matrix $ A \in {\mathbb R}^{n \times n} $ A ∈ R 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. [ABSTRACT FROM AUTHOR]