Stabilization with Decay Estimate for Second-Order Bilinear Systems with Time Delay

This paper is concerned with stabilization with energy decay rates of a class of second-order bilinear systems with time delay in a Hilbert space. We study strong and exponential stabilization with bilinear feedback controls. First, we rely on the cosine family to establish the well-posedness of the resulting closed-loop system. Then, we provide sufficient conditions under which the chosen control strategy achieves strong or exponential stabilization of the system. In addition, in the case of the strong stabilization, an explicit decay estimate is established. The obtained results are finally illustrated by wave and beam equations with simulation as applications.