Robust pole placement via polytope of reflection vectors

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 polynomials coefficients 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.