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 http://resolver.caltech.edu/CaltechAUTHORS:MCLieeetac97
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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.
|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|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Archive Administrator|
|Deposited On:||29 Jan 2007|
|Last Modified:||26 Dec 2012 09:30|
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