A sufficient condition is derived such that the closed-loop state delayed system is stable and guarantees a prescribed H-infinity norm bound of the closed-loop transfer matrix from the disturbance to the controlled output. Based on this derivation, a full-order observer-based H-infinity controller for the state delayed linear systems is constructed by solving two modified algebraic Riccati equations. The state feedback H-infinity controller for the state delayed linear systems is also obtained by solving a modified algebraic Riccati equation. An illustrative example is given to show the applicability of the proposed approach.