Global Stabilization of Linear Systems with Bounds on the Feedback and its Successive Derivatives

Abstract

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 $p\in\mathbb N$, 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 a positive real part. This generalizes previous work done for single-input chains of integrators and rotating dynamics.