This paper deals with the design of linear systems with saturating actuators where the actuator limitations have to be incorporated a priori into control design, We take a semiglobal approach to solve some of the central control problems for such systems, These problems include stabilization, input-additive disturbance rejection, and robust stabilization in the presence of matched nonlinear uncertainties, We develop further the semiglobal design technology which was initiated in our earlier work [7] and utilize it to deal with these control problems.