Robust Strictly Positive Real Synthesis for Convex Combination of Sixth-Order Polynomials

Abstract

For the two sixth-order polynomials $a(s)$ and $b(s),$ 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. Our reasoning method is constructive, and is insightful and helpful in solving the general robust strictly positive real synthesis problem.