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In this article, we present rapid boundary stabilization of a Timoshenko beam with antidamping and antistiffness at the uncontrolled boundary, by using infinite-dimensional backstepping. We introduce a Riemann transformation to map the Timoshenko beam states into a set of coordinates that verify a 1-D hyperbolic PIDE-ODE system. Then backstepping is applied to obtain a control law guaranteeing closed-loop stability of the origin in the L{2} sense. Arbitrarily rapid stabilization can be achieved by adjusting control parameters, and has not been achieved in previous results. Finally, a numerical simulation shows the effectiveness of the proposed controller. This result extends a previous work which considered a slender Timoshenko beam with Kelvin-Voigt damping, by allowing destabilizing boundary conditions at the uncontrolled boundary and attaining an arbitrarily rapid convergence rate. © 1963-2012 IEEE.
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IEEE Transactions on Automatic Control
ISSN: 0018-9286
Year: 2024
Issue: 2
Volume: 69
Page: 1141-1148
6 . 8 0 0
JCR@2022
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WoS CC Cited Count: 0
SCOPUS Cited Count: 4
ESI Highly Cited Papers on the List: 0 Unfold All
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30 Days PV: 3
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