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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:
93D20Asymptotic stability of control systems
93C10Nonlinear control systems
93C99Control systems, guided systems
93-02Research monographs (systems and control)
37C75Stability theory