Finding the Nearest Passive or Nonpassive System via Hamiltonian Eigenvalue Optimization

DOI10.1137/20M1376972zbMath1483.65097arXiv2010.15954OpenAlexW3214320698MaRDI QIDQ5014162

Antonio Fazzi, Christian Lubich, Nicola Guglielmi

Publication date: 1 December 2021

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.15954

zbMATH Keywords

Hamiltonian matricesmatrix nearness problemstructured eigenvalue optimizationdistance to nonpassivitypassive control systemstructured passivity enforcement

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Linear systems in control theory (93C05) Eigenvalue problems (93B60) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items (2)

Computation of the nearest structured matrix triplet with common null space ⋮ Root-Max Problems, Hybrid Expansion-Contraction, and Quadratically Convergent Optimization of Passive Systems

Uses Software

• SLICOT
• PSAPSR

Cites Work

• Unnamed Item
• Unnamed Item
• A Schur decomposition for Hamiltonian matrices
• A bisection method for computing the \(H_{\infty}\) norm of a transfer matrix and related problems
• On computing the distance to stability for matrices using linear dissipative Hamiltonian systems
• Stability radii for real linear Hamiltonian systems with perturbed dissipation
• A projector-splitting integrator for dynamical low-rank approximation
• Low rank differential equations for Hamiltonian matrix nearness problems
• Numerical Linear Algebra Methods for Linear Differential-Algebraic Equations
• Discretized Dynamical Low-Rank Approximation in the Presence of Small Singular Values
• Stability Radii for Linear Hamiltonian Systems with Dissipation Under Structure-Preserving Perturbations
• Perturbation Theory for Hamiltonian Matrices and the Distance to Bounded-Realness
• Fast Algorithms for the Approximation of the Pseudospectral Abscissa and Pseudospectral Radius of a Matrix
• Derivatives and Perturbations of Eigenvectors
• Passivity Enforcement via Perturbation of Hamiltonian Matrices
• Matrix Stabilization Using Differential Equations
• Finding the Nearest Positive-Real System
• Dissipativity Enforcement via Perturbation of Para-Hermitian Pencils
• Dynamical Low‐Rank Approximation

This page was built for publication: Finding the Nearest Passive or Nonpassive System via Hamiltonian Eigenvalue Optimization