Stability regions of nonlinear autonomous dynamical systems
A topological and dynamical characterization of the stability boundaries for a fairly large class of nonlinear autonomous dynamic systems is presented. The stability boundary of a stable equilibrium point is shown to consist of the stable manifolds of all the equilibrium points (and/or closed orbits...
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Veröffentlicht in: | IEEE transactions on automatic control 1988-01, Vol.33 (1), p.16-27 |
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Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | A topological and dynamical characterization of the stability boundaries for a fairly large class of nonlinear autonomous dynamic systems is presented. The stability boundary of a stable equilibrium point is shown to consist of the stable manifolds of all the equilibrium points (and/or closed orbits) on the stability boundary. Several necessary and sufficient conditions are derived to determine whether a given equilibrium point (or closed orbit) is on the stability boundary. A method for finding the stability region on the basis of these results is proposed. The method, when feasible, will find the exact stability region, rather than a subset of it as in the Lyapunov theory approach. Several examples are given to illustrate the theoretical prediction.< > |
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ISSN: | 0018-9286 1558-2523 |
DOI: | 10.1109/9.357 |