An Application of Rouche's Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials

An important problem related to the study of the robust stability of a linear system that presents variation in terms of an uncertain parameter consists of understanding the variation in the roots of a system's characteristic polynomial in terms of the uncertain parameter. In this contribution, we propose an algorithm to provide sufficient conditions on the uncertain parameter in such a way that a robustly stable family of polynomials has all of its zeros inside a specific subset of its stability region. Our method is based on the Rouche's theorem and uses robustly stable polynomials constructed by using basic properties of orthogonal polynomials.