This book considered the H control problem for vehicle active suspension systems (the quarter vehicle model, the vertical model of half-vehicle, the vertical model of Full-vehicle) over a finite frequency domain, since these systems aim the improvement of the vehicle ride comfort, also we design a state-return controller based on linear matrix inequalities (LMIS) such as the resulting closed-loop system is asymptotically stable. Based on the generalized Kalman_Yacubovich_Popov(GKYP) Lemma. The H performance is analyzed to measure the ride comfort of the vehicle and to improve the ride comfort, the H norm is decreased in specific frequency band [4 8] hz. Our theoretical methods are formulated as a linear matrix inequalities(LMIS). The theoretical results are illustrated as simulation results to show the effectiveness of the proposed method.