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

Abstract

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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> 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).