ON MAPPABLE NONLINEARITIES IN ROBUSTNESS ANALYSIS

When carrying out robustness analysis in the frequency domain, the fol lowing fundamental problem arises: Given a description of the uncertai n quantities entering the system, at each frequency omega, we need to carry out a mapping into the complex plane. For the special case of mu ltilinear uncertainty structures, the Mapping Theorem greatly facilita tes this process and leads to the convex hull of the value set of inte rest. In this paper, we generalize the class of nonlinear uncertainty structures for which the convex hull can be generated-the so-called Ge neralized Mapping Theorem goes considerably beyond the multilinear set ting. For example, this new framework leads to mappability for large c lasses of polynomic and nonlinear uncertainty structures, The formulas associated with convex hull generation are seen to be easily implemen ted in two-dimensional graphics.