Global stabilization of classes of linear control systems with bounds on the feedback and its successive derivatives

Abstract : In this paper, we address the problem of globally stabilizing a linear time-invariant (LTI) system by means of a static feedback law whose amplitude and successive time derivatives, up to a prescribed order p, are bounded by arbitrary prescribed values. We solve this problem for two classes of LTI systems, namely integrator chains and controllable skew-symmetric systems with single input. For the integrator chains, the solution we propose is based on the nested saturations introduced by A.R. Teel. We show that this construction fails for skew-symmetric systems and propose an alternative feedback law. We illustrate these findings by the stabilization of the third order integrator and the harmonic oscillator with prescribed bounds on the feedback and its first two derivatives.
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Systems and Control Letters, Elsevier, 2017, 99, pp.17-24. 〈10.1016/j.sysconle.2016.11.002〉
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Soumis le : mardi 12 juin 2018 - 17:02:08
Dernière modification le : jeudi 7 février 2019 - 14:45:24

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Jonathan Laporte, Antoine Chaillet, Yacine Chitour. Global stabilization of classes of linear control systems with bounds on the feedback and its successive derivatives. Systems and Control Letters, Elsevier, 2017, 99, pp.17-24. 〈10.1016/j.sysconle.2016.11.002〉. 〈hal-01633370〉

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