Stability radius for extended linearization with system uncertainty

The problem considered is the computation of the stability radius for a class of nonlinear systems which have been brought under extended linearization and are subject to matrix perturbations that are either structured or unstructured. A method to obtain an upper bound for the radius of stability in extended linearization based on overvaluing a comparison system (Metzlerian) is proposed. It is shown that the stability radius around a suitable domain can be obtained by computing the largest singular value of an overvalued matrix that posses special properties.