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

Abstract

Under the assumption that A+AT 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 ATK+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+AT. A possible improvement is also proposed and a numerical example is presented to illustrate the new result.