A lower bound for the solution of the algebraic Riccati equation of optimal control and a geometric convergence rate for the Kleinman algorithm

A new sharp lower bound for the solution of the algebraic Riccati equation of optimal control is presented for the case when the state cost matrix
Q
is positive definite. The bound is easier to evaluate than previous sharp bounds. It is then used in the derivation of a geometric convergence rate for the Kleinman algorithm (an iterative method for solving the algebraic Riccati equation).