A new method for the design of stabilizing controllers for multivariable bilinear systems is presented. The design method is based on a Liapunov stability theorem and the solution of a Liapunov equation. The resulting non-linear control globally asymptotically stabilizes the closed-loop system and minimizes a generalized quadratic performance index. The effect of the weighting matrices on the closed-loop response is analysed. Simulation results demonstrate that the new design technique provides better control than linear feedback. Moreover, the linear feedback can destabilize the closed-loop system depending on the initial conditions, whereas the new control strategy results in global asymptotic stability.