Communications in Information and Systems
Volume 1 (2001)
Homotopy for the $\nu$-gap
Pages: 333 – 380
The main result of this paper is to show that a “winding number condition” which relates to two strictly multivariable linear operators, and which is used in the definition of the Vinnicombe ($\nu$-gap) metric, is equivalent to the existence of a multivariable homotopy in the same metric between the two operators. This allows a characterisation of the Vinnicombe metric which is independent of the linearity of the underlying operators, and suggests possible extension of the metric to nonlinear operators.