# An LMI Condition for the Robustness of Constant-Delay Linear Predictor Feedback with Respect to Uncertain Time-Varying Input Delays

## TL;DR

This paper presents an LMI-based condition ensuring the exponential stability of constant-delay predictor feedback systems under uncertain time-varying delays, extending to certain boundary control systems.

## Contribution

It introduces a new LMI condition for robustness of predictor feedback with uncertain delays, applicable to infinite-dimensional boundary control systems.

## Key findings

- LMI condition guarantees stability for small delay variations
- Method extends to boundary control systems with time-varying delays
- Provides a systematic approach for robust predictor feedback design

## Abstract

This paper discusses the robustness of the constant-delay predictor feedback in the case of an uncertain time-varying input delay. Specifically, we study the stability of the closed-loop system when the predictor feedback is designed based on the knowledge of the nominal value of the time-varying delay. By resorting to an adequate Lyapunov-Krasovskii functional, we derive an LMI-based sufficient condition ensuring the exponential stability of the closed-loop system for small enough variations of the time-varying delay around its nominal value. These results are extended to the feedback stabilization of a class of diagonal infinite-dimensional boundary control systems in the presence of a time-varying delay in the boundary control input.