Some Preliminary Results on Robust Reflection Coefficients Placement

Abstract

A new version of pole placement controller design, called robust reflection coefficients placement, is proposed for discrete-time systems. Instead of a single stable point a stable simplex must be preselected in the closed loop characteristic polynomials coefficients space. A constructive procedure for generating simplexis inside the "nice stability region" is given starting from the unit hypercube of reflection coefficients of monic polynomials. This procedure is quite straightforward: an appropriate stable point has to be chosen and then the edges of the stable simplex will be generated by a linear Schur invariant transformation. The procedure of robust controller design makes use of a stability measure defined as the minimal distance between a preselected stable simplex and vertices of an uncertain interval plant.