Lab Papers (GRASP)

Document Type

Conference Paper

Date of this Version

12-15-2006

Comments

Copyright 2006 IEEE. Reprinted from:
Loizou, S.G.; Jadbabaie, A., "Density Functions for Navigation Function Based Systems," Decision and Control, 2006 45th IEEE Conference on , vol., no., pp.1800-1805, 13-15 Dec. 2006
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=4178003&isnumber=4176993

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Abstract

In this paper, we present a scheme for constructing density functions for systems that are almost globally asymptotically stable (i.e., systems for which all trajectories converge to an equilibrium except for a set of measure zero) based on navigation functions. Although recently-proven converse theorems guarantee the existence of density functions for such systems, results are only existential and the construction of a density function for almost globally asymptotically stable systems remains a challenging task. We show that for a specific class of dynamical systems that are defined based on a navigation function, a density function can be easily derived from the system's underlying navigation function

Keywords

asymptotic stability, functions, navigation, density functions, dynamical system, globally asymptotically stable system, navigation function based system

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Date Posted: 23 September 2009