Controllability and stability radii for companion form systems

DOI10.1007/BF02551286zbMath0657.93007OpenAlexW1981482844MaRDI QIDQ1111496

Alan J. Laub, Charles S. Kenney

Publication date: 1988

Published in: MCSS. Mathematics of Control, Signals, and Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02551286

zbMATH Keywords

controllabilitystabilizabilitysingular valuesrobustness measurescompanion form matricesfinite-dimensional linear state-space systems

Mathematics Subject Classification ID

Sensitivity (robustness) (93B35) Controllability (93B05) Stabilization of systems by feedback (93D15) Canonical structure (93B10) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items (16)

Eigenvalue condition numbers and pseudospectra of Fiedler matrices ⋮ Robust pole placement in discrete-time systems ⋮ An implicit deflation method for ill-conditioned Sylvester and Lyapunov equations ⋮ Condition numbers for inversion of Fiedler companion matrices ⋮ Two algorithms for finding the Hermitian reflexive and skew-Hermitian solutions of Sylvester matrix equations ⋮ A class of boundary perturbations described by bounded operators ⋮ Direct block tridiagonalization of single-input single-output systems ⋮ Estimating the distance to uncontrollability: A fast method and a slow one ⋮ An algorithm for computing the distance to uncontrollability ⋮ The feedback search algorithm: estimating the distance of semi-explicit systems to \(\mathcal{R}\)-uncontrollability ⋮ Inheritance properties of Krylov subspace methods for continuous-time algebraic Riccati equations ⋮ A global minimum search algorithm for estimating the distance to uncontrollability ⋮ Controllability Radii of Linear Systems with Constrained Controls Under Structured Perturbations ⋮ Iterative algorithm for the reflexive solutions of the generalized Sylvester matrix equation ⋮ Nonscalar matrix polynomial representation of some scalar polynomials ⋮ Bounds for eigenvalues of matrix polynomials

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stability radius for structured perturbations and the algebraic Riccati equation
• Between controllable and uncontrollable
• On condition numbers and the distance to the nearest ill-posed problem
• Stability radii of linear systems
• The geometry of ill-conditioning
• Smallest destabilizing perturbations for linear systems
• On the solution of a class of algebraic matrix Riccati equation
• Perturbation bounds for robust stability in linear state space models
• Characterization and efficient computation of the structured singular value
• State-space measures for stability robustness
• A Schur method for solving algebraic Riccati equations
• Properties of numerical algorithms related to computing controllability
• On the solution of the discrete-time Lyapunov matrix equation in controllable canonical form
• A counterexample for two conjectures about stability

This page was built for publication: Controllability and stability radii for companion form systems