A unified approach to eigenvalue bounds of the solution of the Riccati equation

Abstract

A unified approach is introduced to measure the eigenvalue bounds of the algebraic Riccati equation. Via deriving eigenvalue bounds of the solution of the socalled “unified Riccati equation”, new upper and lower extreme eigenvalue bounds for the solutions of the continuous and discrete Riccati matrix equations are proposed. It is shown that some of the presented bounds for the continuous Riccati equation are sharper than the majority of existing results and the upper bound for the maximum eigenvalue of the solution of the discrete Riccati equation is less restrictive than parallel results in some cases.