Standard J-spectral factorization of rational matrices via generalized algebraic riccati equation

Abstract This paper considers a J -spectral factorization problem for a rational spectral matrix. The problem is called the standard J -spectral factorization problem ( S - J - SEP ) since it is applicable to the standard H ∞ control for a descriptor system (DS). A solution to the S - J - SFP is provided in terms of a stabilizing solution of an indefinite generalized algebraic Riccati equation (GARE). The main result of this paper includes the well-known result on the canonical J -spectral factorization problem ( C - J - SFP ).