Selection of a single uniquely specifiable I controller in the chain-scattering framework

This paper studies the notion of central Pa controllers in the chain-scattering framework. Since in the chain-scattering framework the :&a control problem is equivalent to a factorisation problenl that yields non-unique factors, it is important to somehow pin down these factors so that the resulting central controller is uniquely defined and corresponds to the central and minimum-entropy coiltroller frequently discussed in the literature. In so doing, we devise a procedure for the selection of a single uniquely specifiable ,Fm coiltroller in the chain-scattering framework. The chain-scattering frainework is important because it has a distinct advantage over state-space based methods for some applications in that it poses and solves the .;4", coiltrol problem entirely in an operator-theoretic setting, thereby allowing LIS to conte~nplate direct changes of the frequency domain syinbols rather than changes in the corresponding state-space matrices. O 2004 Elsevier Ltd. All rights reserved. Keyivorcis: .F,-control; J-Lossless factorisation; Chain-scattering; Central controller; Miuimum entropy controller