The purpose of this paper is to examine the problem of controlling a l
inear time-invariant system subject to input saturation in order to ha
ve its output track (or reject) a family of reference (or disturbance)
signals produced by some external generator. It is shown that a semig
lobal framework for this problem is a natural one. Within this framewo
rk, a set of solvability conditions are given and feedback laws that s
olve the problem are constructed. The theory developed in this paper i
ncorporates earlier results established for linear systems without inp
ut saturation.