On an upper bound for the eigenvalues of the solution of the continuous algebraic Riccati equation

Under the assumption that A + A(T) is positive semi-definite, Liu et al. (2010) proposed an upper bound for the eigenvalues of the solution K of the continuous algebraic Riccati equation A(T)K + KA -KRK = -Q where Q is positive semi-definite and R is positive definite. In this paper, we complement Liu et al.'s result without assuming the positivity of A+A(T). A possible improvement is also proposed and a numerical example is presented to illustrate the new result. (C) 2022 Elsevier Ltd. All rights reserved.

Automated summary

In this paper, we investigate the eigenvalues of the solution to the continuous algebraic Riccati equation without assuming the positivity of A+A(T). We also propose a possible improvement and provide a numerical example to illustrate the new result.