Upper and lower bounds on the solution of the algebraic Riccati equation

Given an algebraic matrix Riccati equation
A'K+ KA - KBB'K + Q =0
, the fundamental inequalities which are satisfied by the extremal eigenvalues of the positive definite solution
K
, are established. It Is illustrated that these resultant estimations appear to be considerably tighter than previously available results in many cases. Similar results are obtained for the discrete algebraic matrix Riccati equation.