An Invariance Radius for Nonlinear Systems

  • Fritz Colonius
  • Wolfgang Kliemann
Chapter
Part of the Systems & Control: Foundations & Applications book series (SCFA)

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.

Keywords

Nonlinear System Stable Equilibrium Pair Condition Invariant Control Stability Radius 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Fritz Colonius
  • Wolfgang Kliemann

There are no affiliations available

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