The output stabilization problem for a linear system with a time-varying input delay is considered. The interval observer technique is extended to delay control systems and applied for obtaining guaranteed interval estimates of the system state. The procedure of the interval observer design, which is based on resolving of the Silvester's equation, is presented. Interval predictor method is introduced in order to design a linear stabilizing feedback. The control design procedure is based on Linear Matrix Inequalities (LMI). The theoretical results are supported by numerical simulations.