Robustly stabilizing controllers for uncertain linear systems

An examination is made of the problem of robustly stabilizing controllers for uncertain linear plants subjected to H^∞ bounds on the perturbations. Robust stabilization means that the controller stabilizes all plants in a family of perturbed plants. The cases in which the plant to be stabilized is subjected to additive, multiplicative and the so-called `stable-factor´ uncertainties are considered. Although these cases are all particular H^∞ problems which normally require iterative solutions, it is shown that they can all be solved explicitly