Departmental Papers (ESE)


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.

Document Type

Journal Article

Subject Area


Date of this Version

March 2008


Copyright YEAR IEEE. Reprinted from IEEE Transactions on Automatic Control, Volume 53, Issue 2, March 2008, pages 612-617.

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Almost gas systems, density functions, dual Lyapunov techniques, navigation functions (NFs)



Date Posted: 09 April 2008

This document has been peer reviewed.