Convex Combinations of Hurwitz Functions and Its Applications to Robustness Analysis
In this paper, we shall show that a family of analytic functions, constructed from the convex hull of a finite number of vertex functions, will have no zero within a simply-connected region in the complex plane if and only if all its edge functions have no zero within the simply-connected region. The result is in fact a generalization of the Edge Theorem which has been derived for polynomial functions [1,2,3]. We then proceed to show how the result can be used to analyse the stability of uncertain systems.
KeywordsComplex Plane Convex Combination Uncertain System Vertex Function Robustness Analysis
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