A method for the design of linear state feedback laws for bilinear systems is presented. Using a Liapunov approach, a class of stabilizing feedback amplifier matrices is constructed, depending on three positive definite weighting matrices which can be selected freely. The computation of the amplifiers requires the solution, by successive approximations, of an algebraic Riccati equation for which a positive definite solution must be found. The relative magnitudes of the weighting matrices, expressed in terms of scaling factors, constitute the main design parameters. The influence of these parameters on some important dynamic characteristics of the system is analysed, thus allowing to adapt the parameter choice to the specifications of the design.