Controller synthesis technique for systems with affine linear uncertainty

Abstract

The paper deals with the design of compensators that provide a guaranteed level of performance, in the sense of gain and phase margins, for systems with affine linear uncertainty. To achieve this goal, powerful procedures for computing the Bode, Nyquist and Nichols envelopes of a transfer function, whose numerator and denominator polynomials are polytopic polynomials, are first developed by using the convex parpolygonal value set of polynomials with affine linear uncertainty. Using these frequency envelopes, a controller design strategy is then presented with two illustrative examples.