In this contribution, linear input delay system with predictor control is studied. The system has some specific properties. First, the time delay affects only the input variable and not the state one. Second, the integral presented in distributed delay term has an exponential type kernel. In this paper we provide the complete type Lyapunov-Krasovskii functionals that take into account these specific properties of the system. The functionals are applied to derive exponential bounds for the solutions of the system.