Communications in Information and Systems

Volume 1 (2001)

Number 4

Homotopy for the $\nu$-gap

Pages: 333 – 380

DOI: http://dx.doi.org/10.4310/CIS.2001.v1.n4.a1

Authors

Thomas S. Brinsmead (RSISE, Australian National University, Canberra, Australia)

Brian D. O. Anderson (RSISE, Australian National University, Canberra, Australia)

Abstract

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.

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