A general result on the stabilization of linear systems using bounded controls

We present two constructions of controllers that globally stabilize linear systems subject to control saturation. The only conditions imposed are the obvious necessary ones, namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition holds. We use essentially arbitrary saturations σ, subject only to the requirement that: (i) σ is locally Lipschitz, (ii) sσ(s)>0 whenever s≠0, (iii) σ is differentiable at 0 and σ´(0)>0, and (iv) lim inf_|s|→∞|σ(s)|>0