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