The Discrete Algebraic Riccati Equation and Hermitian Block Toeplitz Matrices

DOI10.1007/978-3-0348-0221-5_22zbMath1252.15018OpenAlexW129708216MaRDI QIDQ2915207

Leonid Lerer, André C. M. Ran

Publication date: 21 September 2012

Published in: A Panorama of Modern Operator Theory and Related Topics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-0348-0221-5_22

zbMATH Keywords

Stein equationdiscrete algebraic Riccati equationHermitian block Toeplitz matrix

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Toeplitz, Cauchy, and related matrices (15B05)

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Cites Work

• The non-symmetric discrete algebraic Riccati equation and canonical factorization of rational matrix functions on the unit circle
• Inertia characteristics of self-adjoint matrix polynomials
• Discrete generalized algebraic Riccati equations and polynomial matrix factorization
• A new inertia theorem for Stein equations, inertia of invertible Hermitian block Toeplitz matrices and matrix orthogonal polynomials
• Inertia theorems for matrices, controllability, and linear vibrations
• Existence and uniqueness of unmixed solutions of the discrete-time algebraic Riccati equation
• Linear Quadratic Problems with Indefinite Cost for Discrete Time Systems
• A Parametrization of Solutions of the Discrete-time Algebraic Riccati Equation Based on Pairs of Opposite Unmixed Solutions
• Order reduction of discrete-time algebraic Riccati equations with singular closed loop matrix
• Unmixed Solutions of the Discrete-Time Algebraic Riccati Equation
• Hermitian solutions of the discrete-time algebraic Riccati equation
• A Generalization of the Inertia Theorem
• On the Structure of the Solutions of Discrete-Time Algebraic Riccati Equation With Singular Closed-Loop Matrix
• Asymmetric algebraic Riccati equation: A homeomorphic parametrization of the set of solutions
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