Algebraic Riccati equation and J-spectral factorization for H_infinity estimation

In this paper we investigate on the existence of the stabilizing solution of the algebraic Riccati equation (ARE) related to the H_infinity filtering problem with a prescribed attenuation level g. It is well known that such a solution exists and is positive definite for g larger than a certain g_F and it does not exist for g smaller than a certain g_0. We consider the intermediate case g in (g_0,g_F] and show that in this interval the stabilizing solution does exist, except for a finite number of values of g. 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_infinity filtering problem.