Density Functions for Navigation Function Based Systems

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