Computing the nearest $\hat{I}\text{c◯}$-admissible descriptor dissipative Hamiltonian system

Abstract

For a given set $\hat{I}\text{c◯}\subseteq \mathbb{C}$, a matrix pair $(E,A)$ is called $\hat{I}\text{c◯}$-admissible if it is regular, impulse-free and its eigenvalues lie inside the region $\hat{I}\text{c◯}$. In this paper, we provide a dissipative Hamiltonian characterization for the matrix pairs that are $\hat{I}\text{c◯}$-admissible where $\hat{I}\text{c◯}$ is an LMI region. We then use these results for solving the nearest $\hat{I}\text{c◯}$-admissible matrix pair problem: Given a matrix pair $(E,A)$, find the nearest $\hat{I}\text{c◯}$-admissible pair $(\tilde{E},\tilde{A})$ to the given pair $(E,A)$. We illustrate our results on several data sets and compare with the state of the art.

24 pages, 6 figures, code available from https://gitlab.com/ngillis/nearest-omega-stable-pair