Robust Pole Placement via Reflection Axes Polytopes

A robust version of the output controller design for discrete-time systems is introduced. Instead of a single stable point a stable polytope is preselected in the closed loop characteristic polynomial coefficient space. A constructive procedure for generating stable polytopes is given starting from the unit hypercube of reflection coefficients of monic polynomials. This procedure is quite straightforward because for a special family of polynomials the linear cover of so-called reflection vectors is stable. The roots placement of reflection vectors is studied. A stability measure in a polytope is introduced in order to solve the problem by quadratic programming approach.