Complete Solution to the General Robust Strictly Positive Real Synthesis Problem for Polynomial Segments

2002/10/30 by Long Wang, Wang, Long
Computer Science · Engineering · Mathematics · #93B15 #93B45 #93D30 #Advanced Optimization Algorithms Research #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC) #Polynomial and algebraic computation #Stability and Control of Uncertain Systems #math.DS #math.OC #msc:93B15 #msc:93B45 #msc:93D30

paper · pdf · doi:10.48550/arxiv.math/0210452

In this paper, a long-standing open problem in modern control theory has been constructively resolved

arxiv created 2002/10/30 · openalex publication_date 2002/10/30 · arxiv updated 2012/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any two n-th order polynomials a(s) and b(s), the Hurwitz stability of their convex combination is necessary and sufficient for the existence of a polynomial c(s) such that c(s)/a(s) and c(s)/b(s) are both strictly positive real.

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• Robust Strictly Positive Real Synthesis for Polynomial Families of Arbitrary Order
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• Lectures on the Routh-Hurwitz problem
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