Andrew Paice, Fabian Wirth
Robustness of nonlinear systems and their domains of attraction
Preprint series: Berichte aus der Technomathematik 99-06, Universität Bremen
MSC:
34D10 Perturbations
34D05 Asymptotic properties
Abstract:
In this paper we consider the problem of analyzing the robustness of
stability of nonlinear systems with time-varying perturbations.
We show that generically the stability radii
with respect to time-varying perturbations of the nonlinear
system and its linearization coincide. A brief introduction to a method
for the calculation of the linear stability radius is presented.
Furthermore, we consider the problem of determining a robust domain of attraction
for the fixed point of a perturbed system under the assumption that the perturbations do not
destroy exponential stability. We discuss some topological properties of the robust
domain of attraction and present an approximation scheme for its
determination.


Keywords: nonlinear systems, perturbations, domain of attraction, robust stability, Lyapunov exponents