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

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Abstract
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 /spl sigma/, subject only to the requirement that: (i) /spl sigma/ is locally Lipschitz, (ii) s/spl sigma/(s)>0 whenever s/spl ne/0, (iii) /spl sigma/ is differentiable at 0 and /spl sigma/'(0)>0, and (iv) lim inf/sub |s|/spl rarr//spl infin//|/spl sigma/(s)|>0.