Observer design and practical stability of nonlinear systems under unknown time-delay

TL;DR

This paper develops an observer design for nonlinear systems with unknown time delays, establishing practical exponential stability using Lyapunov-Krasovskii functionals, supported by simulations and a physical model.

Contribution

It introduces a new observer design method for time-delay nonlinear systems and provides sufficient conditions for practical stability, validated through simulations and a physical example.

Findings

Observer achieves exponential convergence despite delays.

Lyapunov-Krasovskii functionals ensure practical stability.

Simulation and physical model confirm feasibility.

Abstract

In the present paper, we study observer design and we establish some sufficient conditions for practical exponential stability for a class of time-delay nonlinear systems written in triangular form. In case of delay, the exponential convergence of the observer was confirmed. Based on the Lyapunov-Krasovskii functionals, the practical stability of the proposed observer is achieved. Finally, a physical model and simulation findings show the feasibility of the suggested strategy.