Robust strictly positive real synthesis of polynomial segments for discrete time systems

By using the result of robust strictly positive real synthesis of polynomial segments for continuous time systems, it is proved that, for any two n-th order polynomials a(z) and b(z), the Schur stability of their convex combination is necessary and sufficient for the existence of an n-th order polynomial c(z) such that c(z)/a(z) and c(z)/b(z) are both strictly positive real. We also provide the construction method of c(z). Illustrative examples are provided to show the effectiveness of this method.