On the robust output control via reflection vectors

A robust version of the output controller design for discrete-time systems is introduced. Instead of a single point a stable polytope (or simplex) is defined in the closed loop characteristic polynomial coefficients space. A constructive procedure for generating simplexes in the "nicely stable" region 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. If the stable simplex is preselected then the robust controller design task is solved by quadratic programming approach. If the stable simplex (or poytope) of reflection vectors is not given then a simple search procedure is needed.