Robustness of Nonlinear Systems and Their Domains of Attraction
In this chapter we consider the problem of analyzing the robustness of stability of nonlinear systems with respect to time-varying perturbations. We show that generically the stability radii of a singular fixed point of the nonlinear system and that of the corresponding 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.
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