Robust Schur Stability and Robust H^2 Performance

In this paper we address the problems of robust stability androbust QTR H^2 performance for uncertain discrete time systemswith nonlinear parametric uncertainties. We consider two families ofsystems with parametric uncertainties described by state space modelswhich offer a fairly general representation of most uncertain systemswith one or two parameters (the approach can be extended to more parameters).For these two families we obtain explicit expressions for the Schurstability radius and for the QTR H^2 robust performance radiusin the case of uncertainties with a single parameter. Moreover, we providea line search algorithm for the these two problems in case of two parameters.Both for the robust stability and the robust performance probelm, explicitnecessary and sufficient conditions are derived. An illustrative exampledemonstrates the algorithms.