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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
asymptotic stability, functions, navigation, density functions, dynamical system, globally asymptotically stable system, navigation function based system
Savvas G. Loizou and Ali Jadbabaie, "Density Functions for Navigation Function Based Systems", . December 2006.
Date Posted: 23 September 2009