On stability robustness of discrete-time systems: the complex-variable approach of Mastorakis

The key element of Mastorakis´ approach is the well-known theorem of Rouche: Suppose f(z) and d(z) are analytic in domain D and on its simple closed boundary ∂D, and suppose that |d(z)|<|f(z)| on ∂D. Then f(z) and f(z)+d(z) have the same number of zeros in D. By taking the nominal and perturbed denominator polynomials of a stable discrete-time transfer function as f(z) and f(z)+d(z), respectively, and taking the unit disk as D, Rouche´s theorem is directly connected to a stability-robustness study. This paper proposes an enhanced complex-variable approach initiated by Mastorakis to derive several improved bounds for stable coefficient perturbations of a nominal Schur polynomial