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