Andrew Paice, Fabian Wirth
Analysis of the Local Robustness of Stability for Maps
The paper is published: Proceedings of the ECC'97, paper no. 334, session TU-E-B-4, Brussels, 1997
93D09 Robust stability
93C10 Nonlinear
In this paper the problem of
measuring the robustness of stability for a perturbed discrete time
nonlinear system is studied. Various stability radii are introduced
and their values for the nonlinear system and its linearization are
compared and it is shown that they generically coincide. 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, discrete nonlinear systems, linearization, genericity, semi-algebraic sets