Nonlinear continuous integral-derivative observer

TL;DR

This paper introduces a high-order nonlinear continuous integral-derivative observer that estimates multiple integrals and derivatives of signals with finite-time stability, robustness, and noise rejection, validated through analysis and simulations.

Contribution

It presents a novel integral-derivative observer based on finite-time stability and singular perturbation techniques, enabling synchronous estimation of integrals and derivatives.

Findings

Ensures finite-time stability of the observer.

Demonstrates robustness against stochastic noise.

Shows effective estimation through simulations.

Abstract

In this paper, a high-order nonlinear continuous integral-derivative observer is presented based on finite-time stability and singular perturbation technique. The proposed integral-derivative observer can not only obtain the multiple integrals of a signal, but can also estimate the derivatives. Conditions are given ensuring finite-time stability for the presented integral-derivative observer, and the stability and robustness in time domain are analysed. The merits of the presented integral-derivative observer include its synchronous estimation of integrals and derivatives, finite-time stability, ease of parameters selection, sufficient stochastic noises rejection and almost no drift phenomenon. The theoretical results are confirmed by computational analysis and simulations.