Sufficient conditions for the simultaneous stabilization of a polytope of systems

Abstract Sufficient conditions for the existence and non-existence of a fixed-order controller stabilizing a polytope of systems are addressed in this paper. To achieve this goal, a solution based on the Hermite–Biehler theorem and an adaptation of the Edge theorem allows us to treat this issue as a simple interpolation problem of stable polynomials. Then, feasibility and infeasibility certificates are established from a reformulation of the interpolation conditions, which enable us to conclude the existence or non-existence of a compensator directly from the points to interpolate.