Global Stabilization of Linear 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

We address the global stabilization of linear time-invariant (LTI) systems when the magnitude of the control input and its successive time derivatives, up to an arbitrary order p ∈ N, are bounded by prescribed values. We propose a static state feedback that solves this problem for any admissible LTI systems, namely for stabilizable systems whose internal dynamics has no eigenvalue with positive real part. This generalizes previous work done for single-input chains of integrators and rotating dynamics.

Keywords: Bounded control; Bounded control rate; Linear systems; Stabilization of systems

Domains: Automatic

Jonathan Laporte, Antoine Chaillet, Yacine Chitour. Global Stabilization of Linear Systems with Bounds on the Feedback and its Successive Derivatives. SIAM Journal on Control and Optimization, 2017, 55 (5), pp.2783 - 2810. ⟨10.1137/16M1070141⟩. ⟨hal-01633364⟩