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Nontangency-based Lyapunov tests for convergence and stability in systems having a continuum of equilibria

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Title Nontangency-based Lyapunov tests for convergence and stability in systems having a continuum of equilibria
 
Creator BHAT, SP
BERNSTEIN, DS
 
Subject linear-systems
stabilization
networks
 
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.
 
Publisher SIAM PUBLICATIONS
 
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
 
Type Article
 
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
 
Language en