An Alternative Proof of the SPR Synthesis Theorem for Polynomial Segments of Arbitrary Order

Abstract

For any positive integer n and any two monic real Hurwitz polynomials of degree n, every convex combination of the two is Hurwitz stable if and only if there exists a common numerator of degree n that makes both endpoint transfer functions strictly positive real. We give a unified proof based on convex separation, contact interpolation, and analytic properties of weakly positive real functions.