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Title: High-Frequency Nonlinear Vibrational Control
Authors: Shapiro, Benjamin
Zinn, B. T.
Type: Article
Keywords: Method of averaging
naturally occurring feedback
nonlinear control
open loop
Issue Date: Jan-1997
Publisher: IEEE
Citation: Shaprio, B. and B.T. Zinn. High Frequency Nonlinear Vibrational Control. IEEE Transactions on Automatic Control, vol42, no1, pg83-90, Jan 1997.
Abstract: This paper discusses the feasibility of high-frequency nonlinear vibrational control. Such control has the advantage that it does not require state measurement and processing capabilities that are required in conventional feedback control. Bellman et al. [1] investigated nonlinear systems controlled by linear vibrational controllers and proved that vibrational control is not feasible if the Jacobian matrix has a positive trace. This paper extends previous work to include nonlinear vibrational controllers. A stability criteria is derived for nonlinear systems with nonlinear controllers, and it is shown that a nonlinear vibrational controller can stabilize a system even if the Jacobian matrix has a positive trace.
Required Publisher Statement: Copyright © [1997] IEEE. Reprinted from IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 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 Maryland '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 By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
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