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

Jonathan Laporte (1) , Antoine Chaillet (1) , Yacine Chitour (2)

1 L2S - Laboratoire des signaux et systèmes
2 Université Paris-Saclay

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.

Mots clés: Oscillators; Global stabilization; Bounded controls; Rate saturation; Multiple integrators

Domaines: Automatique / Robotique

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, 2017, 99, pp.17-24. ⟨10.1016/j.sysconle.2016.11.002⟩. ⟨hal-01633370⟩