A general result on the stabilization of linear systems using bounded controls. Sussmann, H.; Sontag, E.; and Yang, Y. IEEE Trans. Automat. Control, 39(12):2411–2425, 1994.
abstract   bibtex   
We present two constructions of controllers that globally stabilize linear systems subject to control saturation. We allow essentially arbitrary saturation functions. The only conditions imposed on the system are the obvious necessary ones, namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition hold. One of the constructions is in terms of a "neural-network type" one-hidden layer architecture, while the other one is in terms of cascades of linear maps and saturations.
@ARTICLE{MR1337566,
   AUTHOR       = {H.J. Sussmann and E.D. Sontag and Y. Yang},
   JOURNAL      = {IEEE Trans. Automat. Control},
   TITLE        = {A general result on the stabilization of linear systems 
      using bounded controls},
   YEAR         = {1994},
   OPTMONTH     = {},
   OPTNOTE      = {},
   NUMBER       = {12},
   PAGES        = {2411--2425},
   VOLUME       = {39},
   KEYWORDS     = {saturation, neural networks, global stability, 
      nonlinear stability},
   PDF          = {../../FTPDIR/saturated-stab.pdf},
   ABSTRACT     = { We present two constructions of controllers that 
      globally stabilize linear systems subject to control saturation. We 
      allow essentially arbitrary saturation functions. The only conditions 
      imposed on the system are the obvious necessary ones, namely that no 
      eigenvalues of the uncontrolled system have positive real part and 
      that the standard stabilizability rank condition hold. One of the 
      constructions is in terms of a "neural-network type" one-hidden layer 
      architecture, while the other one is in terms of cascades of linear 
      maps and saturations. }
}
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