Time-Varying Input and State Delay Compensation for Uncertain Nonlinear Systems

TL;DR

This paper presents a robust control method for uncertain nonlinear systems with unknown, time-varying state delays and known input delays, ensuring stability and bounded tracking despite disturbances.

Contribution

It introduces a delay compensation technique using integral control and Lyapunov-Krasovskii functionals for uncertain nonlinear systems with time-varying delays.

Findings

Guarantees bounded tracking under bounded, slowly varying delays.

Develops a delay-free error system using integral control.

Provides stability analysis with Lyapunov-Krasovskii functionals.

Abstract

A robust controller is developed for uncertain, second-order nonlinear systems subject to simultaneous unknown, time-varying state delays and known, time-varying input delays in addition to additive, sufficiently smooth disturbances. An integral term composed of previous control values facilitates a delay-free open-loop error system and the development of the feedback control structure. A stability analysis based on Lyapunov-Krasovskii (LK) functionals guarantees uniformly ultimately bounded tracking under the assumption that the delays are bounded and slowly varying.