Rapid stabilizability of infinite-dimensional control systems with time delays

In this paper, we investigate the rapid stabilizability of linear infinite-dimensional control systems with a constant time delay. Under the assumptions that the state operator generates an immediately compact semigroup and that the delay coefficient is constant, we establish two main results: (i) The presence of a time-delay term does not affect the rapid stabilizability of the control system; that is, this property depends only on the state and control operators; (ii) Static feedback is sufficient to achieve rapid stabilization of the system. Applications are also presented.