The robust root locus

A simple technique is described for generating the root loci of a feedback system which includes perturbations q∈R^l entering affine linearly into the coefficients of the plant. Denoting the perturbed plant by P(s, q) and the compensator by C(s), the authors address the following problem: given a bounding set Q⇐R^l for q, find the locus of points z in the complex plane such that 1+kP(z, q)C(z)=0 for some k⩾0 and some q∈Q. Such points z are said to lie on the robust root locus. One of the strengths of the technique presented is that it avoids the combinatoric explosion synonymous with gridding the l-dimensional set Q and plotting a large number of ordinary root loci associated with the points. Instead, it exploits only a 2-d gridding of a bounded subset of the complex plane