Abstract
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.
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Paice, A.D.B., Wirth, F.R. Analysis of the local robustness of stability for flows. Math. Control Signal Systems 11, 289–302 (1998). https://doi.org/10.1007/BF02750394
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DOI: https://doi.org/10.1007/BF02750394