Abstract
The stability radius of linear differential equations gives a measure for the robustness of stability with respect to (real, complex, or dynamic) perturbations. In this chapter a generalization for asymptotically stable equilibria of nonlinear systems is proposed and analyzed. It specifies the maximal perturbation range, for which the control set surrounding the equilibrium retains its invariance. It is shown that this value is attained when the invariant control set touches the boundary of its invariant domain of attraction. Then it merges with another (variant) control set and itself becomes variant.
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Colonius, F., Kliemann, W. (2001). An Invariance Radius for Nonlinear Systems. In: Colonius, F., Helmke, U., Prätzel-Wolters, D., Wirth, F. (eds) Advances in Mathematical Systems Theory. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0179-3_5
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DOI: https://doi.org/10.1007/978-1-4612-0179-3_5
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6649-5
Online ISBN: 978-1-4612-0179-3
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