From identification to robust control in the behavioral framework

Summary form only given. Our approach to identification is based on the assumption that an upper bound on the norm of the perturbation affecting the data is a priori known. As a consequence, an uncertain family of systems is obtained with norm bounded uncertainty. The kernel representations of the systems belonging to this uncertain family form a convex set. Two robust control methods are explored. The first is based on results regarding the robust strict-positive realness property of a class of rational functions. This method allows the computation of a controller which maximizes the stability margin, using Ritz-type methods. A relationship between the optimal stability margin and (an appropriate measure of) the size of the uncertain family can thus be derived. The second method uses results of the H_∞ problem in a behavioral setting. We present the above concepts for the case of systems with 2 external variables (SISO systems), together with examples showing the trade-off between the size of the uncertainty and the optimal stability margin