Stability Radii for Linear Hamiltonian Systems with Dissipation Under Structure-Preserving Perturbations

DOI10.1137/16M1067330zbMath1349.93332MaRDI QIDQ2834693

Christian Mehl, Volker Mehrmann, Punit Sharma

Publication date: 23 November 2016

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

zbMATH Keywords

distance to instabilityport-Hamiltonian systemdissipative Hamiltonian systemrestricted distance to instabilitystructure-preserving distance to instability

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Asymptotic stability in control theory (93D20) Robust stability (93D09) Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical methods for differential-algebraic equations (65L80) Canonical forms, reductions, classification (15A21)

Related Items

Error bounds for port-Hamiltonian model and controller reduction based on system balancing ⋮ Computation of the nearest structured matrix triplet with common null space ⋮ On the Closest Stable/Unstable Nonnegative Matrix and Related Stability Radii ⋮ Stability and distance to instability for polynomial matrix families. Complex perturbations ⋮ Stability radii for real linear Hamiltonian systems with perturbed dissipation ⋮ On computing the distance to stability for matrices using linear dissipative Hamiltonian systems ⋮ A non-intrusive method to inferring linear port-Hamiltonian realizations using time-domain data ⋮ Large-Scale Estimation of Dominant Poles of a Transfer Function by an Interpolatory Framework ⋮ On Non-Hermitian Positive (Semi)Definite Linear Algebraic Systems Arising from Dissipative Hamiltonian DAEs ⋮ Control of port-Hamiltonian differential-algebraic systems and applications ⋮ Approximating the nearest stable discrete-time system ⋮ Hypocoercivity and controllability in linear semi‐dissipative Hamiltonian ordinary differential equations and differential‐algebraic equations ⋮ Structure-preserving \(\mathcal{H}_{\infty}\) control for port-Hamiltonian systems ⋮ The hypocoercivity index for the short time behavior of linear time-invariant ODE systems ⋮ Explicit port-Hamiltonian formulation of multi-bond graphs for an automated model generation ⋮ Identification of port-Hamiltonian systems from frequency response data ⋮ Unnamed Item ⋮ Generalized port-Hamiltonian DAE systems ⋮ Maximal Acyclic Subgraphs and Closest Stable Matrices ⋮ Robust port-Hamiltonian representations of passive systems ⋮ Finding the Nearest Positive-Real System ⋮ Large-Scale and Global Maximization of the Distance to Instability ⋮ Approximation of stability radii for large-scale dissipative Hamiltonian systems ⋮ Numerical mathematics and control. Preface to a special issue dedicated to Volker Mehrmann on the occasion of his 65th birthday ⋮ Minimal-norm static feedbacks using dissipative Hamiltonian matrices ⋮ Distance problems for dissipative Hamiltonian systems and related matrix polynomials ⋮ Linear Algebra Properties of Dissipative Hamiltonian Descriptor Systems ⋮ Computing Closest Stable Nonnegative Matrix ⋮ Structured Backward Errors for Eigenvalues of Linear Port-Hamiltonian Descriptor Systems ⋮ Finding the Nearest Passive or Nonpassive System via Hamiltonian Eigenvalue Optimization ⋮ Estimation of Structured Distances to Singularity for Matrix Pencils with Symmetry Structures: A Linear Algebra--Based Approach ⋮ Random perturbations of matrix polynomials

Uses Software

• CVX

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Linear port-Hamiltonian systems on infinite-dimensional spaces.
• Damped oscillations of linear systems. A mathematical introduction
• Stability radius for structured perturbations and the algebraic Riccati equation
• A Newton-based method for the calculation of the distance to instability
• A framework for the solution of the generalized realization problem
• Exploiting structure in large-scale electrical circuit and power system problems
• Stability radii of linear systems
• An intrinsic Hamiltonian formulation of network dynamics: Non-standard Poisson structures and gyrators
• Backward perturbation analysis of certain characteristic subspaces
• Hamiltonian formulation of distributed-parameter systems with boundary energy flow
• Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems
• Linearization of DAEs along trajectories
• Port-Hamiltonian Systems on Graphs
• Structured Eigenvalue Backward Errors of Matrix Pencils and Polynomials with Hermitian and Related Structures
• μ-Values and Spectral Value Sets for Linear Perturbation Classes Defined by a Scalar Product
• Mathematical Systems Theory I
• Structured Mapping Problems for Matrices Associated with Scalar Products. Part I: Lie and Jordan Algebras
• Matrix Analysis
• A Bisection Method for Measuring the Distance of a Stable Matrix to the Unstable Matrices
• On Representations and Integrability of Mathematical Structures in Energy-Conserving Physical Systems
• An Algorithm for Computing the Distance to Instability
• Matrices Which Take a Given Vector into a Given Vector: Revisited
• Structural analysis of electric circuits and consequences for MNA
• Port-Hamiltonian Differential-Algebraic Systems
• Approximation of Large-Scale Dynamical Systems