This paper presents an approach to design multiobjective static output feedback H ₂/ H _∞/ GH ₂ controller for vehicle suspensions by using linear matrix inequalities (LMIs) and genetic algorithms (GAs). A quarter-car model with active suspension system is studied in this paper and three main performance requirements for an advanced vehicle suspension are considered. Among these requirements, the ride comfort performance is optimized by minimizing the H ₂ norm from the road disturbance to the sprung mass acceleration, the road holding performance is improved by constraining the H _∞ norm from the road disturbance to the tyre deflection to be less than a given value, and the suspension deflection is guaranteed to be less than its hard limit by constraining the generalized H ₂ norm from the road disturbance to the suspension deflection. In addition, the controller gain can be constrained naturally in GAs, which can avoid the actuator saturation problem. A static output feedback controller, which only uses the available sprung velocity and suspension deflection signals as feedback signals, is obtained. This multiobjective controller is realized by using GAs to search for the possible control gain matrix and then to resolve the LMIs together with the minimization optimization problem. The approach is validated by numerical simulation which shows that the designed static output feedback controller can achieve good active suspension performances in spite of its simplicity.