On quadratic Hurwitz stability of segment polynomials

Whether the Hurwitz stability of segment polynomials implies the quadratic stability is an interesting subject in relating to the Lyapunov route to Kharitonov´s theorem. Noting that segment polynomial families associated with a strictly positive real function are not only stable, but quadratically stable independently of their length, we have examined if such is possible with nonpositive real functions, taking second-degree polynomials. The answer is that the quadratic stability independent of the length implies and is implied by the positive realness. Based on this fact, we have shown that even second-degree interval polynomials cannot always be quadratically stable