A general result on the stabilization of linear systems using bounded controls. Sussmann, H., Sontag, E., & 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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