Frequency Domain Criteria for Robust Root Locations of Generalized Disc Polynomials

Abstract

This paper derives a frequency domain criterion for Hurwitz stability of polynomials with complex coefficients in L p domains for a fixed real p ∈ [1,∞] (generalized disc polynomials). The frequency domain criterion only requires one frequency domain plot to check the robustness of generalized disc polynomials for all real p ∈ [1,∞]. Furthermore the largest allowable perturbation bounds for all real p ∈ [1,∞] can be graphically estimated from the same frequency domain plot. The frequency domain criterion is then extended to constrain a specified number of roots of a set of disc polynomials to lie within specific domains in the complex plane. This is especially useful in computing lower bounds in applications like dominant pole assignment and filter design where poles are required to be placed in several simply connected domains which do not intersect each other.