Robust reflection coefficients placement by quadratic programming

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 simplices inside the nice stability region is given starting from the unit hypercube of reflection coefficients of monic polynomials. This procedure is quite straightforward because, first, 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 by quadratic programming makes use of a stability measure defined as the minimal distance between a preselected stable simplex and vertices of an uncertain interval plant.