Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2005-10

June 2005

Irrational transfer function classes, coprime factorization and stabilization

Amol J. Sasane

Classes of irrational function classes, denoted by As, that lie between the extreme cases of the disk algebra A and the Hardy space Hinfinity(D), are considered. The corona theorem holds for As, and the following properties are shown: As is an integral domain, but not a Bézout domain, As is a Hermite ring with stable rank 1, and the Banach algebra As has topological stable rank 2. Consequences to the coprime factorization of transfer functions and stabilizing controller synthesis using a factorization approach are discussed.

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Last modified: 3rd June 2005