On the robust control of polytopic plants

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 closed loop characteristic polynomials coefficients space. A constructive procedure for generating a simplex 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 coefficients 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