article · Evolution equations and control theory
The strong stabilizability of linear second order equation is investigated in this paper. It is supposed that there exists a linear feedback law that makes the origin of the closed-loop system globally asymptotically stable. Then this control is subject to a cone-bounded nonlinearity. Well-posedness and stability results of the closed-loop system under such (nonlinear) control are stated. The first result is proven by using nonlinear semigroups techniques and the Schauder fixed-point theorem and the second one is based on the result of Marx et al. [12]. Our results are then applied to the particular damped and undamped wave equation. Simulation results are presented to validate the theoretical results. Note that some of the results of this paper apply for a large class systems.
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DOI: 10.3934/eect.2023006
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