Algebraic Riccati equation and J-spectral factorization for H-infinity estimation

摘要

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 gamma. It is well known that such a solution exists and is positive definite for gamma larger than a certain gamma(F) and it does not exist for gamma smaller than a certain gamma(0). We consider the intermediate case gamma is an element of (gamma(0), gamma(F)] and show that in this interval the stabilizing solution does exist, except for a finite number of values of gamma. 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. (C) 2003 Elsevier B.V. All rights reserved. [References: 10]