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Convergence is the property whereby every solution converges to a limit point that may depend on the initial condition. Semistability is the additional requirement that all solutions converge to limit points that are Lyapunov stable. We give new Lyapunov-function-based results for convergence and semistability of nonlinear systems.

These results do not make assumptions of sign definiteness on the Lyapunov function. Instead, our results use a novel condition based on nontangency between the vector field and invariant or negatively invariant subsets of the level or sublevel sets of the Lyapunov function or its derivative and represent extensions of previously known stability results involving semidefinite Lyapunov functions.

To illustrate our results we deduce convergence and semistability of the kinetics of the Michaelis--Menten chemical reaction and the closed-loop dynamics of a scalar system under a universal adaptive stabilizing feedback controller. Sign in Help View Cart.

Dynamical Systems Introduction

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Email to a friend. Digg This. Notify Me! E-mail Alerts. RSS Feeds. SIAM J. Control Optim. Related Databases. Web of Science You must be logged in with an active subscription to view this. Keywords nontangency , Lyapunov stability , semistability , convergence , prolongations. Publication Data. ISSN print : Publisher: Society for Industrial and Applied Mathematics.

ISBN 13: 9789056991722

Sanjay P. Bhat and Dennis S.

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Journal of Nonlinear Science 29 :4, Rafal Goebel and Ricardo G. Automatica 81 , International Journal of Control 89 :6, Control Theory and Technology. The work by the second author was partially supported by NSF Grants no. Journal of the Franklin Institute :3, Book summary views reflect the number of visits to the book and chapter landing pages.

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Cited by. Crossref Citations. This book has been cited by the following publications. This list is generated based on data provided by CrossRef. Wang, Tao and Chiang, Hsiao-Dong Sohn, Alexandre P. Abrantes, Adriano L. Alberto, Luis F. Stability region of a wind power system under low-voltage ride-through constraint. Yumagulov, M. Mustafina, I. A study of the boundaries of stability regions in two-parameter dynamical systems. Automation and Remote Control, Vol. Siahaan, Sahat P and Pangaribuan, Timbang Stabilization of nonlinear system using uniform eigenvalue assignment in linear model.

Stability analysis of a wind power system via PEBS method. Fisher, Michael W. Parametric dependence of large disturbance response and relationship to stability boundary. Wang, Shuo and Chiang, Hsiao-Dong Amaral, Fabiolo M. Ibragimova, L. Journal of Mathematical Sciences, Vol. Google Scholar Citations. Scopus Citations. Export citation Recommend to librarian Recommend this book. Stability Regions of Nonlinear Dynamical Systems.

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