2023-03-222023-03-222022Chen, G., Vázquez Valenzuela, R. y Krstic, M. (2022). Backstepping-Based Exponential Stabilization of Timoshenko Beam with Prescribed Decay Rate. En 4th IFAC Workshop on Control of Systems Governed by Partial Differential Equations, CPDE 2022, IFAC-PapersOnLine, 55 (26) (162-167)2405-8963https://hdl.handle.net/11441/143524This is an open access article under the CC BY-NC-ND license.In this paper, we present a rapid boundary stabilization of a Timoshenko beam with anti-damping and anti-stiffness at the uncontrolled boundary, by using PDE backstepping. We introduce a transformation to map the Timoshenko beam states into a (2+2) × (2+2) hyperbolic PIDE-ODE system. Then backstepping is applied to obtain a control law guaranteeing closed-loop stability of the origin in the H1 sense. Arbitrarily rapid stabilization can be achieved by adjusting control parameters. Finally, a numerical simulation shows that the proposed controller can rapidly stabilize the Timoshenko beam. This result extends a previous work which considered a slender Timoshenko beam with Kelvin-Voigt damping, allowing destabilizing boundary conditions at the uncontrolled boundary and attaining an arbitrarily rapid convergence rate.application/pdf6 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/openAccess10.1016/j.ifacol.2022.10.394