• Corpus ID: 115168542

# Extension of the $\nu$-metric

@article{Ball2010ExtensionOT,
title={Extension of the \$\nu\$-metric},
author={Joseph A. Ball and Amol Sasane},
journal={arXiv: Optimization and Control},
year={2010}
}
• Published 27 February 2010
• Mathematics
• arXiv: Optimization and Control
We extend the $\nu$-metric introduced by Vinnicombe in robust control theory for rational plants to the case of infinite-dimensional systems/classes of nonrational transfer functions.

## References

SHOWING 1-10 OF 28 REFERENCES
On the encirclement condition and its generalization
A new sufficiency proof for the Nyquist criterion is obtained via the analyticity properties of the log function. The intuition derived therefrom is then used to formulate a generalized stability
An abstract Nyquist criterion containing old and new results
We prove an abstract Nyquist criterion in a general set up. As applications, we recover various versions of the Nyquist criterion, some of which are new.
On the corona theorem for almost periodic functions
LetAPΣ+(Rn) denote the Banach algebra of all continuous almost periodic functions onRn whose Bohr-Fourier spectrum is contained in an additive semi-group Σ⊂[0, ∞)n. We show that the maximal ideal
Topological and analytical indices in C∗-algebras
Abstract A notion of topological index for the continuous symbol functions of generalized Toeplitz operators is introduced. This generalizes the winding number of functions on the circle and the
Frequency domain uncertainty and the graph topology
• G. Vinnicombe
• Computer Science, Mathematics
IEEE Trans. Autom. Control.
• 1993
A new metric on linear, time-invariant systems is defined. This metric is no greater than the gap metric, and is in fact the smallest metric for which a certain robust stabilization result holds.
Sufficient conditions for the projective freeness of Banach algebras
• Mathematics
• 2009
Let R be a unital semi-simple commutative complex Banach algebra, and let M(R) denote its maximal ideal space, equipped with the Gelfand topology. Sufficient topological conditions are given on M(R)
A lattice approach to analysis and synthesis problems