Robust stability test of polytopic family of polynomials: The Dixon's resultant method

This paper deals with the D-stability test of a polytope of polynomials when the boundary ∂D of a given simple connected domain D in the complex plan is described by a polynomial equation, a problem that covers two special but important cases: Hurwitz stability and Schur stability of a polytope of polynomials. Based on the "Edge Theorem" and the method of Dixon's resultant elimination, a new test approach is presented. By using the presented method, the stability test can be carried out by computing Dixon's resultants and solving linear matrix equations. Two examples are given to demonstrate the approach.