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

DSpace at IIT Bombay

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Title Arc-length-based Lyapunov tests for convergence and stability in systems having a continuum of equilibria
 
Creator BHAT, SP
BERNSTEIN, DS
 
Subject linear-systems
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. In this paper, we relate convergence and stability to arc length of the orbits. More specifically, we show that a system is convergent if all of its orbits have finite are length, while an equilibrium is Lyapunov stable if the arc length (considered as a function of the initial condition) is continuous at the equilibrium, and semistable if the arc length is continuous in a neighborhood of the equilibrium. Next we derive arc-length-based Lyapunov results for convergence and stability. These results do not require the Lyapunov function to be positive definite. Instead, these results involve an inequality relating the righthandside of the differential equation and the Lyapunov function derivative. This inequality makes it possible to deduce properties of the arc length function and thus leads to sufficient conditions for convergence and stability. Finally, we give additional assumptions under which the converses of all the main results hold.
 
Publisher IEEE
 
Date 2011-10-25T10:21:58Z
2011-12-15T09:11:47Z
2011-10-25T10:21:58Z
2011-12-15T09:11:47Z
2003
 
Type Proceedings Paper
 
Identifier PROCEEDINGS OF THE 2003 AMERICAN CONTROL CONFERENCE, VOLS 1-6,2961-2966
0-7803-7896-2
0743-1619
http://dspace.library.iitb.ac.in/xmlui/handle/10054/15688
http://hdl.handle.net/100/2288
 
Source Annual American Control Conference (ACC 2003),DENVER, CO,JUN 04, 2003-JUN 06, 2006
 
Language English