Eigenvalue bounds for algebraic Riccati and Lyapunov equations
- 1 April 1982
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 27 (2), 461-463
- https://doi.org/10.1109/tac.1982.1102947
Abstract
The majorization result of Wimmer [2] relating the eigenvalues of the matrices involved in the Lyapunov equation is extended to the algebraic Riccati equation. This result, coupled with certain results on the eigenvalue bounds for sum and product of matrices, yields several lower and upper bounds for the eigenvalues of the solution matrix of the algebraic Riccati and Lyapunov equations.Keywords
This publication has 9 references indexed in Scilit:
- Upper and lower bounds on the solution of the algebraic Riccati equationIEEE Transactions on Automatic Control, 1979
- On norm bounds for algebraic Riccati and Lyapunov equationsIEEE Transactions on Automatic Control, 1978
- A note on the algebraic matrix Riccati equationIEEE Transactions on Automatic Control, 1977
- Generalizations of theorems of Lyapunov and SteinLinear Algebra and its Applications, 1975
- On the Lyapunov matrix equationIEEE Transactions on Automatic Control, 1974
- Control System Analysis and Design Via the “Second Method” of Lyapunov: I—Continuous-Time SystemsJournal of Basic Engineering, 1960
- Extreme properties of eigenvalues of a Hermitian transformation and singular values of the sum and product of linear transformationsDuke Mathematical Journal, 1956
- Maximum Properties and Inequalities for the Eigenvalues of Completely Continuous OperatorsProceedings of the National Academy of Sciences, 1951
- On a Theorem of Weyl Concerning Eigenvalues of Linear TransformationsProceedings of the National Academy of Sciences, 1950