Robust control via polytopic stability region approximations

A robust version of the output controller design for discrete-time systems is introduced. Instead of a single stable point a stable polytope (or simplex) is preselected in the closed loop characteristic polynomials coefficients space. A constructive procedure for generating stable simplexis 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 a stable target simplex is preselected then the robust output controller design task is solved by quadratic programming approach.