Standard J-Spectral Factorization of Rational Matrices via Generalized Algebraic Riccati Equation

In this paper we consider a J-spectral factorization problem for a rational spectral matrix. The problem considered here is called the standard J-spectral factorization problem (S-J-SFP) since it is applicable to the standard H∞ control problem for a descriptor system (DS). Based on DS representation of the spectral matrix, we derive a solution to the S-J-SFP using a stabilizing solution of an indefinite generalized algebraic Riccati equation (GARE). The main result of this paper includes the well-known solution to the canonical J-spectral factorization problem (C-J-SFP).