Global stabilization of multiple integrators by a bounded feedback with constraints on its successive derivatives

TL;DR

This paper presents a method for globally stabilizing chains of integrators using a bounded feedback law with constraints on its derivatives, ensuring control amplitudes stay within prescribed limits.

Contribution

It introduces a nested saturation-based feedback design that guarantees bounded control and derivatives, extending stabilization techniques to higher-order integrator chains.

Findings

Control amplitude and derivatives can be bounded below any prescribed limits.

The method successfully stabilizes third-order integrator with bounded feedback and derivatives.

The approach generalizes to chains of integrators with constraints on control signals.

Abstract

In this paper, we address the global stabilization of chains of integrators by means of a bounded static feedback law whose p first time derivatives are bounded. Our construction is based on the technique of nested saturations introduced by Teel. We show that the control amplitude and the maximum value of its p first derivatives can be imposed below any prescribed values. Our results are illustrated by the stabilization of the third order integrator on the feedback and its first two derivatives.