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).
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