Computing frequency responses of uncertain systems

A numerical approach is proposed for computing the frequency-response templates of a class of rational transfer functions whose coefficients are affine functions of some interval parameters. This approach is based on characterizing the template as the set of points in the complex plane that make the value set of a certain polytope of polynomials to include the origin. With this characterization, the proposed approach traces out the boundary of the frequency-response template corresponding to a single frequency by using a simple pivoting procedure along with an efficient zero-inclusion test algorithm.