Robustness of nonlinear systems subject to time-varying perturbations

We introduce time-varying stability for nonlinear systems. Using linearization techniques and spectral theory for time-varying linear systems it is shown that the nonlinear stability radius is bounded by two linear stability radii. The set of matrices for which these two stability radii differ has measure zero. At the moment it is not known, whether this set is open. For extended stability radii with respect to different guaranteed exponential growth rates similar results are obtained.