Abstarct: Active control methods are the new and effective methods in the control of vibration of the building and the structures under the effects of earthquake and high wind .One of the fundamental parameters of the active control systems , that affects the performance of such systems , is synchronization of incoming data from the sensor and outgoing controlling command from the controllers to the actuators .However there is a time delay between the the incoming and outgoing signals of the control system , which is due to the natural characteristics of the system hardware .The time delay decrease the stability and overall performance of the control system.In this work,to suppress or improve the undesired effects of the time delay , study on the most important and new methods , such as optimal control with predictive performance index and Lqr performance index ,root locus, phase-shift ,pade approximation ,state-augmented , recursive response , smith’s predictor and controllability baxsed stabilization method ,has been accomplished .The research indicates that the optimal control algorithms make better improvement with respect to the non-optimal control and are suitable for the large time delays .while in the non-optimal control algorithms , if the time delay become large ,the stability of the controlled structures wouldn’t be guaranteed .