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Title:Almost Lyapunov functions
Author(s):Ying, Charles
Advisor(s):Liberzon, Daniel M.; Zharnitsky, Vadim
Department / Program:Electrical & Computer Eng
Discipline:Electrical & Computer Engr
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Lyapunov stability
negativity of Lyapunov derivative
partial information
Abstract:An autonomous, time-invariant dynamical system that verifies the classical Lyapunov criterion is globally asymptotically stable for the case when the Lyapunov function is strictly decreasing along the solution. We define an almost Lyapunov function to be a candidate Lyapunov function whose derivative with respect to time is of unknown sign in a set of small measure and negative elsewhere. We investigate the convergence of a system associated with an almost Lyapunov function. We show that for an unknown set of small enough measure, all the trajectories converge to a ball around the equilibrium point, under standard condition of Lipschitz continuity over the system and the derivative of the almost Lyapunov function.
Issue Date:2014-01-16
Rights Information:Copyright 2013 Charles Ying
Date Available in IDEALS:2014-01-16
Date Deposited:2013-12

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