Robust Hurwitz stability of a class of complex polynomials arising from H∞ control theory

Abstract This paper deals with the Hurwitz stability of a class of complex polynomials arising from H∞ control theory. Using an isomorphic transformation between the complex variables, sufficient and necessary conditions are obtained on the basis of the Sylvester resultant. Moreover, by applying the complete discrimination system for real polynomials, algebraic criteria for the Hurwitz stability can be derived easily. Unlike the known methods with which the stability test involves infinitely many testing steps, our method provides a testing procedure that needs only a finite number of testing steps. As an application, the presented method has been used successfully to study the problem of H∞ Hurwitz stabilization, a problem of simultaneous stabilization of the closed‐loop characteristic polynomial, and a family of complex polynomials of our concern.