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.

翻译：对于给定集合$\Omega \subseteq \mathbb{C}$，若矩阵对$(E,A)$是正则的、无脉冲的且其特征值位于区域$\Omega$内部，则称其为$\Omega$-容许的。本文针对$\Omega$为线性矩阵不等式（LMI）区域的情形，给出了$\Omega$-容许矩阵对的耗散哈密顿系统表征。基于此结果，我们进一步求解最近$\Omega$-容许矩阵对问题：给定矩阵对$(E,A)$，寻找与给定对$(E,A)$距离最近的$\Omega$-容许对$(\tilde E, \tilde A)$。我们在多个数据集上验证了所提方法的有效性，并与现有最优方法进行了比较。