ON ROBUST CONTROL AND NICE STABILITY VIA REFLECTION COEFFICIENTS
Ülo Nurges · Proceedings of the Estonian Academy of Sciences Physics Mathematics · 1999
A robust version of the modal controller design for discrete-time systems is introduced.Instead of a single stable point a stable simplex must be preselected in the coefficients space of closed-loop characteristic polynomials.A constructive procedure for generating simplexes 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, n edges are generated by a linear Schur invariant transformation and, second, the most critical edge is determined by the difference of reflection coefficient numbers.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 polytopic plant.