This paper presents an approach to design static output feedback and non-fragile static output feedback H∞ controllers for active vehicle suspensions by using linear matrix inequalities and genetic algorithms. A quarter-car model with active suspension system is considered in this paper. By suitably formulating the minimization problem of the sprung mass acceleration, suspension deflection and tyre deflection, a static output feedback H∞ controller and a non-fragile static output feedback H∞ controller are obtained. The controller gain is naturally constrained in the design process. The approach is validated by numerical simulation which shows that the designed static output feedback H ∞ controller can achieve good active suspension performance in spite of its simplicity, and the non-fragile static output feedback H ∞ controller has significantly improved the non-fragility characteristics over controller gain variations. © 2003 Elsevier Ltd. All rights reserved.