Global Stabilization of Nonlinear Delay Systems With a Compact Absorbing Set

TL;DR

This paper introduces a predictor-based control scheme for nonlinear delay systems that ensures global stability, robustness, and exponential convergence, even with sampled and delayed measurements, using an approximate predictor expressed by integral delay equations.

Contribution

It presents a novel control scheme combining an inter-sample predictor, a global observer, and an approximate predictor for nonlinear systems with input delays and compact absorbing sets.

Findings

Achieves global asymptotic stability and exponential convergence.

Demonstrates robustness to sampling schedule perturbations and measurement errors.

Extends to systems transformable to those with a compact absorbing set.

Abstract

Predictor-based stabilization results are provided for nonlinear systems with input delays and a compact absorbing set. The control scheme consists of an inter-sample predictor, a global observer, an approximate predictor, and a nominal controller for the delay-free case. The control scheme is applicable even to the case where the measurement is sampled and possibly delayed. The closed-loop system is shown to have the properties of global asymptotic stability and exponential convergence in the disturbance-free case, robustness with respect to perturbations of the sampling schedule, and robustness with respect to measurement errors. In contrast to existing predictor feedback laws, the proposed control scheme utilizes an approximate predictor of a dynamic type which is expressed by a system described by Integral Delay Equations. Additional results are provided for systems that can be transformed to systems with a compact absorbing set by means of a preliminary predictor feedback.