ON SOME ASPECTS OF THE J-SPECTRAL FACTORIZATION

The J-spectral factorization problem naturally arises in control theory and it plays an important role in H(infinity)-control, linear quadratic optimal control, Hankel norm approximation problem. Characterization of solution for control problems is sometimes given using the J-spectral factor(s). The paper has the nature of a survey article. We review the band method version of the Grassmannian approach for solving strictly contractive extension problems and the J-spectral factorization approach for solving the suboptimal Nehari problem in the setting of the Wiener algebra on the imaginary axis. The new (and modest) contributions is to clarify the connections between the two approaches.