Abstract: The paper considers optimal vibration control design problem for sampled-data systems with controller-actuator delay and sensor-controller delay in Delta-domain applying the Delta-transform.Firstly,the sampled-data system with time-delays is discretized.By using system transformation and delta operators,the discrete-time time-delay system is converted into a nondelayed one in Delta-domain.Then,the optimal control law of feedforward and feedback optimal vibration is designed by solving a Riccati algebraic equation and a Stein matrix equation of Delta-domain.Finally,the simulation examples illustrate the designed control law can compensate for the effects produced by delays and vibrations.