Robust stability of quasi-polynomials and the finite inclusions theorem

A semianalytic tool for the study of the robust stability of quasi-polynomials of retarded type is presented. The approach is based on graphical methods. The finite Nyquist theorem for polynomials is extended to the case of quasi-polynomials with the help of a novel approach. The finite inclusions theorem for quasi-polynomials is derived. It allows to conclude on the stability of polytopic families of quasi-polynomials from a finite number of testing values.