Departmental Papers (ESE)

Document Type

Journal Article

Date of this Version

March 2008

Comments

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

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.

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.

Keywords

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

Share

COinS
 

Date Posted: 09 April 2008

This document has been peer reviewed.