In this paper we develop fixed-order (i.e. full- and reduced-order) controllers for continuous-time and discrete-time linear systems with actuator amplitude and rate saturation constraints. The problem is formulated as a multiobjective problem involving a convex combination of an L-1 norm and the H-2 norm to capture actuator saturation constraints and closed-loop system performance in the face of exogenous white noise disturbances. The L-1 convolution operator norm considered is induced by bounded amplitude persistent L-infinity disturbances and L-infinity performance variables involving the actuator amplitude and rate signals. Hence, the peak pointwise-in-time actuator amplitude and actuator rate excursion are guaranteed to be less than the product of the L-1 convolution operator norm and the L-infinity disturbance amplitude bound. Application of the proposed framework to the design of multivariable saturation controllers for the control of a bank-to-turn missile and a high-performance fighter aircraft is demonstrated.