Sensitivity analysis of the algebraic Riccati equations

Summary.In this paper, some sharp perturbation bounds for the Hermitian positive semi-definite solution to an algebraic Riccati equation are developed. A further analysis for these bounds is done. This analysis shows that there is, presumably, some intrinsic relation between the sensitivity of the solution to the algebraic Riccati equation and the distance of the spectrum of the closed-loop matrix from the imaginary axis.