Discrete J-spectral factorization

This paper deals with the J-spectral factorization for general discrete rat ional matrices. A simple approach based on the Kalman filtering in Krein sp ace is proposed. The main idea is to construct a stochastic state space fil tering model in Krein space such that the spectral matrix of the output is equal to the rational matrix to be factorized. The spectral factor is then easily derived by using the generalized Kalman filtering in Krein space, wh ich is similar to the H-2 spectral factorization. Our approach unifies the treatment of the H-2 spectral factorization and the J-spectral factorizatio n. The applications of the derived results in H-infinity and risk-sensitive estimation for both nonsingular and singular systems are demonstrated. (C) 2001 Elsevier Science B.V. All rights reserved.