A generalized H-infinity control problem, which covers preview and delayed control strategies, is discussed based on a state-space approach. By introducing a Hamiltonian matrix, which is associated with a delay-free generalized plant, the analytic solution to the corresponding operator Riccati equation is newly established. Based on the result obtained here, the H-infinity control problem is solved and, for typical control problems (e.g., H-infinity and linear quadratic (LQ) control for multiple input delay systems, H-infinity preview control), some interpretations are provided on the resulting control system.