Robust H2 and H∞ filters for uncertain LFT systems

In this paper, the robust H₂ and H_∞ filter design problems are considered, where 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 the results for systems with polytopic uncertainty. It is also shown that for the unstructured, norm bounded uncertainty case, the results here are less conservative than former results, where Riccati equation approach are used. A numerical example is given to illustrate the results.