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On the estimation of asymptotic stability regions: State of the art and new proposals. (English) Zbl 0568.93054
This paper deals with the problem of the estimation of regions of asymptotic stability for continuous nonlinear autonomous systems. The first part of the paper contains a brief survey of existing methods. In the second part a method of reversing the trajectory flow is used combined with simple topological considerations to enlarge an initial arbitrarily small attractive domain. Some low-dimensional examples are considered.
Reviewer: L.Faibusovich

MSC:
93D20 Asymptotic stability in control theory
93C10 Nonlinear systems in control theory
93C99 Model systems in control theory
93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
37C75 Stability theory for smooth dynamical systems
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