Reduction-Based Robustness Analysis of Linear Predictor Feedback for Distributed Input Delays

TL;DR

This paper uses Lyapunov-Krasovskii methods and Artstein's reduction to analyze the robustness of a linear predictor feedback system with distributed input delays, ensuring stability despite parameter and delay mismatches.

Contribution

It introduces a novel functional based on Artstein's reduction to establish delay and parameter robustness of predictor feedback in distributed delay systems.

Findings

Feedback remains stabilizing under small parameter mismatches

Functional depends on norms of reduced and original states

Provides stability guarantees for distributed input delays

Abstract

Lyapunov-Krasovskii approach is applied to parameter- and delay-robustness analysis of the feedback suggested by Manitius and Olbrot for a linear time-invariant system with distributed input delay. A functional is designed based on Artstein's system reduction technique. It depends on the norms of the reduction-transformed plant state and original actuator state. The functional is used to prove that the feedback is stabilizing when there is a slight mismatch in the system matrices and delay values between the plant and controller.