Andrew Paice, Fabian Wirth
Analysis of the Local Robustness of Stability for Flows
The paper is published: Mathematics of Control, Signals and Systems, 11(4):289-302, 1998
93D09 Robust stability
93C10 Nonlinear
In this paper the problem of measuring the robustness of stability
for a perturbed continuous time nonlinear system at a singular fixed
point is studied. Various stability radii are introduced and their
values for the nonlinear system and its linearization are compared.
It is shown that they generically coincide. This result may also be
used to show generic continuity of linear real stability radii.
Some examples are presented showing that it is sometimes necessary
to consider the nonlinear system directly, and not simply to rely on
the information provided by the linearization.

Keywords: Robustness, stability radius, nonlinear systems, linearization, genericity, semi-algebraic sets