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

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