Some new results on algebraic Riccati equations arising in linear quadratic differential games and the stabilization of uncertain linear systems

Abstract

This paper presents some new results on algebraic Riccati equations arising in linear quadratic differential games. The first result is a uniqueness result for solutions of the Riccati equations under consideration. The second result is concerned with Riccati equations which arise in differential games in which the weighting on the minimizing control is allowed to approach zero. It is shown that if a certain minimum phase condition is satisfied then the corresponding solution to the Riccati equation will also approach zero.