A note on Hankel approximation of all-pass functions Original Research Article

The paper extends the results obtained by Fuhrmann and Ober on Hankel approximation. With an arbitrary transfer function G we can associate—using left-and right-coprime factorization—two all-pass functions image and U and also a function R* (called the characteristic function of G) which is connected with the LQG controller of the function G. We analyse the connections between the Hankel operators image, HR* and image, image, and also establish a one-to-one correspondence between the optimal Hankel approximation of HR* and that of image with some additional property. Finally, the duality results on Nehari complements and Hankel approximations are extended.