This article presents a method to control and stabilise systems with pure input lag. The approach is based on a new state predictor which estimates the future of states and guarantees that the prediction error converges asymptotically to zero. The state feedback controller is then designed based on this predictor. Furthermore, a sequential structure of sub-predictors is presented for unstable systems with a long time-delay and accordingly the controller is designed for asymptotic stability. The core idea is to design a series of coupled predictors, each of which is responsible for the prediction of one small portion of the delay, such that the predictors collectively predict the states for a long time-delay. Moreover, sequential sub-predictor method is used for robust control of dead time systems in presence of uncertainty. Simulation examples are presented to verify the proposed method.