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Title: Density functions for navigation-function-based systems
Authors: Jadbabaie, Ali
Loizou, Savvas 
Keywords: Noise--Measurement
Density functionals
Asymptotic theory
Issue Date: 2008
Publisher: IEEE
Source: IEEE Transactions on Automatic Control, 2008, Volume 53, Issue 2, Pages 612-617
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) using navigation functions (NFs). Although recently-proven converse theorems guarantee the existence of density functions for such systems, such 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 an NF, a density function can be easily derived from the system's underlying NF.
ISSN: 00189286
DOI: 10.1109/TAC.2008.917745
Rights: © 2008 IEEE
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