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

TL;DR

This paper characterizes and computes the nearest matrix pair that is $ ext{Omega}$-admissible, ensuring regularity, impulse-freeness, and eigenvalues within a specified LMI region, with applications demonstrated on data sets.

Contribution

It provides a dissipative Hamiltonian framework for $ ext{Omega}$-admissible pairs and introduces a method to find the nearest such pair to a given matrix pair.

Findings

The characterization applies to LMI regions.

The proposed method effectively finds the nearest $ ext{Omega}$-admissible pair.

Results outperform existing approaches on tested data sets.

Abstract

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.