On the numerical properties of the Schur approach for solving the matrix Riccati equation

DOI10.1016/0167-6911(87)90040-5zbMath0635.65043OpenAlexW2102575629MaRDI QIDQ1097641

Petko Hr. Petkov, Nicolai D. Christov, Michael M.Konstantinov

Publication date: 1987

Published in: Systems \& Control Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-6911(87)90040-5

zbMATH Keywords

numerical examplenumerical instabilityHamiltonian matrixSchur methodcontinuous algebraic matrix Riccati equationreduction to upper quasitriangular form

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Matrix equations and identities (15A24) Control/observation systems governed by ordinary differential equations (93C15)

Related Items

A stability-enhancing scaling procedure for Schur-Riccati solvers, A structured condition number for self-adjoint polynomial matrix equations with applications in linear control, Calculation of orthogonal projections and the solution of the matrix algebraic Riccati equation, Discrete generalized algebraic Riccati equations and polynomial matrix factorization, A structure-preserving doubling algorithm for continuous-time algebraic Riccati equations, Error bounds for Newton refinement of solutions to algebraic Riccati equations, How to decompose semi-definite discrete-time algebraic Riccati equations, Generalized Lyapunov equation and factorization of matrix polynomials, Optimization in the Hardy space and the problem of the parametrization of controllers

Uses Software

• EISPACK
• LINPACK
• HQR3
• RICPAC

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Matrix eigensystem routines - EISPACK guide. 2nd ed
• Towards a formal definition of numerical stability
• Perturbation Analysis of Matrix Quadratic Equations
• A LINPACK-style condition estimator for the equation<tex>AX-XB^{T} = C</tex>
• A Schur method for solving algebraic Riccati equations
• On the Separation of Two Matrices
• A Generalized Eigenvalue Approach for Solving Riccati Equations
• Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems