Stabilization of the Timoshenko Beam System with Restricted Boundary Feedback Controls

This paper concerns with the stabilization of a Timoshenko beam with bounded constraints on boundary feedback controls. Since the resulting controlled system is nonlinear, the weak well-posedness is proven by theories of the nonlinear monotone operators and the optimization. Then, the asymptotical stability of the controlled beam is analyzed by the weak topology, and its exponential stability is also proven by the Lyapunov’s second method. In the end, the numerical experiment indicates that the control design is feasible.

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