We study the problem of disturbance attenuation via state feedback for asymptotically stable systems with a saturation nonlinearity in the control channel. The disturbance is assumed to be bounded, with the bound known. This amounts to adding a saturation nonlinearity in the disturbance channel. A sufficient condition is derived in terms of algebraic matrix inequalities, which are much simpler to solve than the general Hamliton-Jacobi-Isaacs partial differential inequality, A suboptimal control law is given based on the solution to the Riccati inequalities. The computational complexity of solving the optimal controller is similar to that of liner H-infinity controller design.