Robust pole assignment via stable polytopes of reflection vectors

Abstract

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 coefficient space of closed-loop characteristic polynomials. A constructive procedure for generating stable simplexes 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 root placement of reflection vectors is studied. If a stable target simplex is preselected, then the robust output controller design task is solved by the quadratic programming approach.