Right invertible multiplication operators and stable rational matrix solutions to an associate Bezout equation. I: The least squares solution

DOI10.1007/s00020-011-1881-4zbMath1293.47027OpenAlexW2064163588MaRDI QIDQ645111

Marinus A. Kaashoek, Arthur E. Frazho, André C. M. Ran

Publication date: 8 November 2011

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00020-011-1881-4

zbMATH Keywords

Toeplitz operatorsstate space representationBezout equationstabilizing solutionstable rational matrix functionsdiscrete algebraic Riccati equationright invertible multiplication operator

Mathematics Subject Classification ID

Operator-theoretic methods (93B28) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators (47A68) Matrix and operator functional equations (39B42)

Related Items (7)

The Algebraic Riccati Equation and Its Role in Indefinite Inner Product Spaces ⋮ Solving continuous time Leech problems for rational operator functions ⋮ Right invertible multiplication operators and stable rational matrix solutions to an associate Bezout equation. I: The least squares solution ⋮ State space formulas for a suboptimal rational Leech problem. I: Maximum entropy solution ⋮ State space formulae for stable rational matrix solutions of a Leech problem ⋮ The Bezout-corona problem revisited: Wiener space setting ⋮ Rational Matrix Solutions of a Bezout Type Equation on the Half-plane

Uses Software

• Matlab

Cites Work

• Right invertible multiplication operators and stable rational matrix solutions to an associate Bezout equation. I: The least squares solution
• Factorization of matrix and operator functions. The state space method
• The non-symmetric discrete algebraic Riccati equation and canonical factorization of rational matrix functions on the unit circle
• Interpolation problems in nest algebras
• Lower bounds in the matrix corona theorem and the codimension one conjecture
• An algorithm for corona solutions on \(H^{\infty}(D)\)
• The matrix-valued \(H^p\) Corona problem in the disk and polydisk
• Interpolations by bounded analytic functions and the corona problem
• State-space solutions to standard H/sub 2/ and H/sub infinity / control problems
• The resultant for regular matrix polynomials and quasi commutativity
• State-space approach to discrete-time,_ℋ∞control
• On contractions similar to isometries and Toeplitz operators
• The Corona Theorem as an Operator Theorem
• State-space solution of the discrete-time minimum entropy control problem via separation
• A matricial corona theorem
• On the Corona Theorem and its Application to Spectral Problems in Hilbert Space
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Right invertible multiplication operators and stable rational matrix solutions to an associate Bezout equation. I: The least squares solution