Stabilization of Nonlinear Delay Systems Using Approximate Predictors and High-Gain Observers

TL;DR

This paper presents a comprehensive output feedback stabilization method for nonlinear systems with long input and output delays, using approximate predictors, high-gain observers, and sampled-data control, ensuring robustness and applicability to linear cases.

Contribution

It introduces a novel global stabilization approach for delayed nonlinear systems employing approximate predictors and high-gain observers, addressing sampling and hold uncertainties.

Findings

Guarantees robustness to sampling schedule perturbations

Applicable to nonlinear systems with sampled measurements

Explicit predictor for linear systems

Abstract

We provide a solution to the heretofore open problem of stabilization of systems with arbitrarily long delays at the input and output of a nonlinear system using output feedback only. The solution is global, employs the predictor approach over the period that combines the input and output delays, addresses nonlinear systems with sampled measurements and with control applied using a zero-order hold, and requires that the sampling/holding periods be sufficiently short, though not necessarily constant. Our approach considers a class of globally Lipschitz strict-feedback systems with disturbances and employs an appropriately constructed successive approximation of the predictor map, a high-gain sampled-data observer, and a linear stabilizing feedback for the delay-free system. The obtained results guarantee robustness to perturbations of the sampling schedule and different sampling and holding periods are considered. The approach is specialized to linear systems, where the predictor is available explicitly.