Computing the nearest Ω-admissible descriptor dissipative Hamiltonian system

2025/11/05 by Nicolas Gillis, Aggarwal, Vaishali, Punit Sharma +2
Computer Science · Mathematics · Engineering · #Matrix Theory and Algorithms #Tensor decomposition and applications #Stability and Control of Uncertain Systems

paper · pdf · doi:10.48550/arxiv.2511.03265

Abstract

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

Citations

• Geometric properties of LMI regions
• Operator Coefficient Methods for Linear Equations
• Finding the nearest Ω-stable pencil with Riemannian optimization

Related

• Linear algebra properties of dissipative Hamiltonian descriptor systems
• Distance problems for dissipative Hamiltonian systems and related matrix polynomials
• Solving matrix nearness problems via Hamiltonian systems, matrix factorization, and optimization
• Computation of the nearest structured matrix triplet with common null space
• Exact density matrix elements for a driven dissipative system described by a quadratic Hamiltonian