Abstract: A finite frequency H_∞ controller with input delay is designed based on the linear matrix inequality method. In the design of finite frequency H_∞ controller, the increase in ride comfort of vehicle and the reduction in car body acceleration are taken as the control target, and the suspension stroke being less than the maximum allowable travel, the wheel keeping well contacted with the ground, and the actuator output being less than the maximum output are taken as the three constraints of control. The influences of control parameters on solving result are analyzed. To solve the problems of that the optimal solution of controller can not be derived from the empirical parameter values, and the parameter values are not universal under different time delay conditions, an optimal design method based on genetic algorithm is proposed, and the performance of controller is analyzed through numeral simulation. The simulated results show that the new proposed finite frequency H_∞ controller optimized by the genetic algorithm can effectively reduce the influence of time delay on control and improve the riding comfort of vehicles in the frequency band of 4-8 Hz. The finite frequency H_∞ controller is obviously superior to the empirically designed controller and the controller without considering the input delay in the control effect. Key

Key words: activesuspension, timedelay, finitefrequencydomain, H_∞control, controlparameter, geneticalgorithm