Title :
Eigenvalue bounds for algebraic Riccati and Lyapunov equations
Author_Institution :
The Bendix Corporation, Englewood, CO, USA
fDate :
4/1/1982 12:00:00 AM
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 :
Algebraic Riccati equation (ARE); Eigenvalues/eigenvectors; Lyapunov matrix equations; Riccati equations, algebraic; Eigenvalues and eigenfunctions; Filtering theory; Linear systems; Matrices; Optimal control; Riccati equations; Stability; Upper bound;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.1982.1102947
