Density Functions for Navigation Function Based Systems
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functions
navigation
density functions
dynamical system
globally asymptotically stable system
navigation function based system
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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
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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 This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.