On convexity of the frequency response of a stable polynomial

Details On convexity of the frequency response of a stable polynomial On convexity of the frequency response of a stable polynomial

2007-09-07

arxiv.org/abs/0709.1064v1

Mathematics

Optimization and Control

Scientific paper

In the complex plane, the frequency response of a univariate polynomial is the set of values taken by the polynomial when evaluated along the imaginary axis. This is an algebraic curve partitioning the plane into several connected components. In this note it is shown that the component including the origin is exactly representable by a linear matrix inequality if and only if the polynomial is stable, in the sense that all its roots have negative real parts.

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