Time-Delay Compensators for Linear Systems with Delayed Output Measurements

TL;DR

This paper introduces a new functional observer design for linear systems with delayed outputs, effectively compensating for sensing latency and enhancing robustness compared to traditional methods.

Contribution

It presents a novel method to extend maximum measurement delay while ensuring stability, with constructive synthesis procedures and extensive numerical validation.

Findings

The observer predicts current state functionals using delayed data.

It extends allowable measurement delays while maintaining stability.

Numerical examples demonstrate the effectiveness of the proposed approach.

Abstract

This paper provides a comprehensive framework for designing functional observers for linear systems subject to delayed output measurements. Moving beyond traditional methodologies, the proposed observer generates an estimate $\hat{z}(t)$ that predicts the current state functional $z(t)=Fx(t)$ using delayed data. By neutralizing sensing latency, the observer serves as a potent time-delay compensator, effectively expanding the practical utility of functional observer theory. The proposed observer architecture offers greater robustness and versatility than traditional Luenberger-type observers by leveraging multiple delayed components to preserve accuracy despite latency. A key contribution of this work is a novel method for extending the maximum allowable measurement delay while maintaining the asymptotic stability of the estimation-error system. Existence conditions are established together with constructive synthesis procedures. Extensive numerical examples are given to illustrate the proposed theory.