A Caltech Library Service

Exponential stabilization of driftless nonlinear control systems using homogeneous feedback

M'Closkey, Robert T. and Murray, Ruchard M. (1997) Exponential stabilization of driftless nonlinear control systems using homogeneous feedback. IEEE Transactions on Automatic Control, 42 (5). pp. 614-628. ISSN 0018-9286. doi:10.1109/9.580865.

PDF - Published Version
See Usage Policy.


Use this Persistent URL to link to this item:


This paper focuses on the problem of exponential stabilization of controllable, driftless systems using time-varying, homogeneous feedback. The analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control Lie algebra. It can be shown that any continuous, time-varying controller that achieves exponential stability relative to the Euclidean norm is necessarily non-Lipschitz. Despite these restrictions, we provide a set of constructive, sufficient conditions for extending smooth, asymptotic stabilizers to homogeneous, exponential stabilizers. The modified feedbacks are everywhere continuous, smooth away from the origin, and can be extended to a large class of systems with torque inputs. The feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers.

Item Type:Article
Related URLs:
URLURL TypeDescription
Murray, Ruchard M.0000-0002-5785-7481
Additional Information:© Copyright 1997 IEEE. Reprinted with permission. Manuscript received May 19, 1995; revised August 16, 1996 and November 8, 1996. Recommended by Associate Editor, J.-B. Pomet. The authors would like to thank L. Praly and the reviewers for their thoughtful comments.
Subject Keywords:Dilation, driftless, exponential stabilization, homogeneous, nonholonomic
Issue or Number:5
Record Number:CaltechAUTHORS:MCLieeetac97
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7316
Deposited By: Archive Administrator
Deposited On:29 Jan 2007
Last Modified:08 Nov 2021 20:41

Repository Staff Only: item control page