A general result on the stabilization of linear systems using bounded controls. Sussmann, H., Sontag, E., & Yang, Y. In Proceedings of 32nd IEEE Conference on Decision and Control, pages 1802–1807 vol.2, December, 1993.
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)\textgreater0 whenever s/spl ne/0, (iii) /spl sigma/ is differentiable at 0 and /spl sigma/'(0)\textgreater0, and (iv) lim inf/sub \textbars\textbar/spl rarr//spl infin//\textbar/spl sigma/(s)\textbar\textgreater0.\textless\textgreater
@inproceedings{sussmann_general_1993,
title = {A general result on the stabilization of linear systems using bounded controls},
doi = {10.1109/CDC.1993.325264},
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){\textgreater}0 whenever s/spl ne/0, (iii) /spl sigma/ is differentiable at 0 and /spl sigma/'(0){\textgreater}0, and (iv) lim inf/sub {\textbar}s{\textbar}/spl rarr//spl infin//{\textbar}/spl sigma/(s){\textbar}{\textgreater}0.{\textless}{\textgreater}},
booktitle = {Proceedings of 32nd {IEEE} {Conference} on {Decision} and {Control}},
author = {Sussmann, H. and Sontag, E. and Yang, Y.},
month = dec,
year = {1993},
keywords = {Actuators, Control systems, Control theory, Eigenvalues and eigenfunctions, Linear systems, Mathematics, Negative feedback, Open loop systems, Power engineering and energy, Power supplies, bounded controls, control saturation, control system analysis, eigenvalues, eigenvalues and eigenfunctions, global stability, linear systems, linear time invariant continuous time systems, stability, stabilization},
pages = {1802--1807 vol.2},
}