Centre for Discrete and Applicable Mathematics |
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CDAM Research Report, LSE-CDAM-2005-10June 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 H(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