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

TL;DR

This paper presents a static state feedback method for globally stabilizing linear systems while ensuring bounds on the control input and its derivatives, extending previous results to more general systems.

Contribution

It introduces a novel feedback approach that guarantees stabilization with bounded control and derivatives for any stabilizable LTI system, generalizing prior specific cases.

Findings

Successfully stabilizes a broad class of LTI systems.

Ensures bounds on control input and derivatives simultaneously.

Extends previous methods from specific systems to general LTI systems.

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 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 positive real part. This generalizes previous work done for single-input chains of integrators and rotating dynamics.