Nontangency-based Lyapunov tests for convergence and stability in systems having a continuum of equilibria
DSpace at IIT Bombay
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Title |
Nontangency-based Lyapunov tests for convergence and stability in systems having a continuum of equilibria
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Creator |
BHAT, SP
BERNSTEIN, DS |
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Subject |
linear-systems
stabilization networks |
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Description |
This paper focuses on the stability analysis of systems having a continuum of equilibria. Two notions that are of particular relevance to such systems are convergence and semistability. 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.
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Publisher |
SIAM PUBLICATIONS
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Date |
2011-08-29T05:23:33Z
2011-12-26T12:58:25Z 2011-12-27T05:48:20Z 2011-08-29T05:23:33Z 2011-12-26T12:58:25Z 2011-12-27T05:48:20Z 2003 |
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Type |
Article
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Identifier |
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 42(5), 1745-1775
0363-0129 http://dx.doi.org/10.1137/S0363012902407119 http://dspace.library.iitb.ac.in/xmlui/handle/10054/11975 http://hdl.handle.net/10054/11975 |
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Language |
en
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