Eigenvalue upper and lower bounds of the solution for the continuous algebraic matrix Riccati equation

A lower bound and several upper bounds of the solution eigenvalues for the continuous algebraic matrix Riccati equation are developed. It is shown that the lower bound is new and tighter than the previous reported one and the upper bounds are concise and less restrictive than the majority of those appeared in the literature. Furthermore, by these results, some bounds for the extreme eigenvalues of the solution matrix of the continuous Lyapunov equation are also defined.