Stratification of full rank polynomial matrices

DOI10.1016/j.laa.2012.12.013zbMath1281.15019OpenAlexW2069830952MaRDI QIDQ389574

Mohammad Hasan, H. S. Yoon

Publication date: 21 January 2014

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2012.12.013

zbMATH Keywords

stratificationlinearizationpolynomial matricesperturbationsmatrix pencilseigenstructure\texttt{StratiGraph}closure hierarchycover relations

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Matrices over function rings in one or more variables (15A54) Matrix pencils (15A22)

Related Items

Block Kronecker linearizations of matrix polynomials and their backward errors, An Algorithm for the Complete Solution of the Quartic Eigenvalue Problem, Structure preserving stratification of skew-symmetric matrix polynomials, Generic symmetric matrix pencils with bounded rank, Generic complete eigenstructures for sets of matrix polynomials with bounded rank and degree, Generic skew-symmetric matrix polynomials with fixed rank and fixed odd grade, Canonical Structure Transitions of System Pencils, Quadratic realizability of palindromic matrix polynomials, Miniversal deformations of pairs of symmetric matrices under congruence, Spectral equivalence of matrix polynomials and the index sum theorem, Minimum norm partial eigenstructure assignment problems in high‐order system via feedback control, Geometry of matrix polynomial spaces, Polynomial zigzag matrices, dual minimal bases, and the realization of completely singular polynomials, Quadratic realizability of palindromic matrix polynomials: the real case, Lyapunov method for stability of descriptor second-order and high-order systems, Change of the congruence canonical form of 2-by-2 and 3-by-3 matrices under perturbations and bundles of matrices under congruence, Generic Symmetric Matrix Polynomials with Bounded Rank and Fixed Odd Grade, Robustness and perturbations of minimal bases. II: The case with given row degrees, Möbius transformations of matrix polynomials, Decoupling of cubic polynomial matrix systems, Van Dooren's Index Sum Theorem and Rational Matrices with Prescribed Structural Data, Matrix Polynomials with Completely Prescribed Eigenstructure, Recovering a perturbation of a matrix polynomial from a perturbation of its first companion linearization

Uses Software

• StratiGraph

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fiedler companion linearizations for rectangular matrix polynomials
• The computation of Kronecker's canonical form of a singular pencil
• On a homeomorphism between orbit spaces of linear systems and matrix polynomials
• Trimmed linearizations for structured matrix polynomials
• Local perturbations of generalized systems under feedback and derivative feedback
• On perturbations and the equivalence orbit of a matrix pencil
• Perturbation of linear control systems
• Fast projection methods for minimal design problems in linear system theory
• Orbit closures of singular matrix pencils
• The algebraic structure of pencils and block Toeplitz matrices
• Limits of generalized state space systems under proportional and derivative feedback
• Methods and algorithms of solving spectral problems for polynomial and rational matrices
• The eigenstructure of an arbitrary polynomial matrix: Computational aspects
• The dimension of matrices (matrix pencils) with given Jordan (Kronecker) canonical forms
• Stratification of linear systems. Bifurcation diagrams for families of linear systems
• The Quadratic Eigenvalue Problem
• Fiedler Companion Linearizations and the Recovery of Minimal Indices
• A Complete Characterization of Orbit Closures of Controllable Singular Systems under Restricted System Equivalence
• Points of Continuity of the Kronecker Canonical Form
• Stratification of Controllability and Observability Pairs—Theory and Use in Applications
• Properties of the system matrix of a generalized state-space system†
• A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part II: A Stratification-Enhanced Staircase Algorithm
• A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part I: Versal Deformations
• Polynomial Roots from Companion Matrix Eigenvalues
• Vector Spaces of Linearizations for Matrix Polynomials
• The Conditioning of Linearizations of Matrix Polynomials
• Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
• Chapter 5: StratiGraph Tool: Matrix Stratifications in Control Applications
• ON MATRICES DEPENDING ON PARAMETERS
• Vehicle Dynamics and Control