Robust H2 and H∞ filters for uncertain LFT systems

In this note, robust H₂ and H_∞ filter design problems are considered. The uncertainties, unstructured or structured, are norm bounded and represented by linear fractional transformation (LFT). The main result is that after upper-bounding the objectives, the problems of minimizing the upper bounds are converted to finite dimensional convex optimization problems involving linear matrix inequalities (LMIs). These are extensions of well-known results for systems with polytopic uncertainty. It is shown that for the unstructured, norm bounded uncertainty case, the upper bounds are directly minimized (without further overbounding), yielding less conservative results than previously available. An elementary numerical example is given to illustrate the results.