169 research outputs found
A refinement of the generalized chordal distance
For single input single output systems, we give a refinement of the
generalized chordal metric. Our metric is given in terms of coprime
factorizations, but it coincides with the extension of Vinnicombe's nu-metric
given in earlier work by Ball and Sasane if the coprime factorizations happens
to be normalized. The advantage of the metric introduced in this article is its
easy computability (since it relies only on coprime factorizations, and does
not require normalized coprime factorizations). We also give concrete
formulations of our abstract metric for standard classes of stable transfer
functions.Comment: 13 page
A generalized chordal metric making strong stabilizability a robust property
An abstract chordal metric is defined on linear control systems described by
their transfer functions. Analogous to a previous result due to Jonathan
Partington ("Robust control and approximation in the chordal metric", in Robust
Control, LNCIS 183, Springer, 1992) for H^infty, it is shown that strong
stabilizability is a robust property in this metric.Comment: 9 pages, 2 figure
On the Bezout equation in the ring of periodic distributions
A corona type theorem is given for the ring R of periodic distributions in
R^d in terms of the sequence of Fourier coefficients of these distributions,
which have at most polynomial growth. It is also shown that the Bass stable
rank and the topological stable rank of R are both equal to 1.Comment: 10 page
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