Computing the nearest $\mathrm{\Omega }$-admissible descriptor dissipative Hamiltonian system

For a given set $\mathrm{\Omega }\subseteq \mathbb{C}$, a matrix pair $(E,A)$ is called $\mathrm{\Omega }$-admissible if it is regular, impulse-free and its eigenvalues lie inside the region $\mathrm{\Omega }$. In this paper, we provide a dissipative Hamiltonian characterization for the matrix pairs that are $\mathrm{\Omega }$-admissible where $\mathrm{\Omega }$ is an LMI region. We then use these results for solving the nearest $\mathrm{\Omega }$-admissible matrix pair problem: Given a matrix pair $(E,A)$, find the nearest $\mathrm{\Omega }$-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.