The non-symmetric discrete algebraic Riccati equation and canonical factorization of rational matrix functions on the unit circle

DOI10.1007/s00020-010-1747-1zbMath1210.47045OpenAlexW2124522014MaRDI QIDQ989946

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

Publication date: 23 August 2010

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

Full work available at URL: https://doi.org/10.1007/s00020-010-1747-1

zbMATH Keywords

Toeplitz operatorsSchur complementsRiccati difference equationcanonical factorizationfinite section methoddiscrete algebraic Riccati equationrational matrix functions

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators (47A68) Difference equations (39A99) Harmonic analysis in one variable (42A99)

Related Items (12)

The Discrete Algebraic Riccati Equation and Hermitian Block Toeplitz Matrices ⋮ Wiener-Hopf indices of unitary functions on the unit circle in terms of realizations and related results on Toeplitz operators ⋮ Factorization of Singular Matrix Polynomials and Matrices with Circular Higher Rank Numerical Ranges ⋮ Solving continuous time Leech problems for rational operator functions ⋮ Wiener-Hopf factorization indices of rational matrix functions with respect to the unit circle in terms of realization ⋮ A Toeplitz-like operator with rational matrix symbol having poles on the unit circle: invertibility and Riccati equations ⋮ 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 ⋮ Canonical factorization of rational matrix functions. A note on a paper by P. Dewilde ⋮ The Bezout-corona problem revisited: Wiener space setting ⋮ Rational Matrix Solutions of a Bezout Type Equation on the Half-plane

Cites Work

• Factorization of matrix and operator functions. The state space method
• Classes of linear operators. Vol. II
• Metric constrained interpolation, commutant lifting and systems
• Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation \(X+A^*X^{-1}A=Q\)
• The stabilizing solution of the discrete algebraic riccati equation
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