In this paper, we develop a static, full-state feedback and a dynamic, outp
ut feedback control design framework for continuous-time, multivariable, li
near, time-invariant systems subject to time-invariant, sector-bounded, inp
ut non-linearities. The proposed framework directly accounts for robust sta
bility and robust performance over the class of input non-linearities. Spec
ifically, the problem of feedback control design in the presence of time-in
variant, sector-bounded, input non-linearities is embedded within a Lure-Po
stnikov Lyapunov function framework by constructing a set of linear-matrix-
inequality conditions whose solution guarantees closed-loop asymptotic stab
ility with guaranteed domains of attraction in the face of time-invariant,
sector-bounded, actuator non-linearities. A detailed numerical algorithm is
provided for solving the linear-matrix-inequality conditions arising in ac
tuator saturation control. Three illustrative numerical examples are presen
ted to demonstrate the effectiveness of the proposed approach.