Algebraic Riccati equation and J-spectral factorization in H-inf estimation

In this paper we investigate on the existence of the stabilizing solution of the algebraic Riccati equation (ARE) related to the H? 5ltering problem with a prescribed attenuation level . It is well known that such a solution exists and is positive de5nite for larger than a certain F and it does not exist for smaller than a certain 0. We consider the intermediate case ? (0; F ] and show that in this interval the stabilizing solution does exist, except for a 5nite number of values of . We show how the solution of the ARE may be employed to obtain a minimum-phase J -spectral factor of the J -spectrum associated with the H? 5ltering problem.