The general γ-attenuation problem is considered for systems with statedependent noise. It is shown that if a controller exists which stabilizes a system with disturbance attenuation then certain LMI's must have positive-definite solutions satisfying a complementary rank condition. If such solutions exist for the considered LMI's the controller is obtained also by solving an LMI. In the absence of the noise the LMI's involved reduce to the ones introduced by Gahinet andalin [7]