# Lower bounds on the maximum delay margin by analytic interpolation

## TL;DR

This paper improves lower bounds on the maximum delay margin in control systems by directly solving an interpolation problem with analytic techniques, avoiding rational approximation steps used in prior work.

## Contribution

The authors develop a direct analytic interpolation approach with domain shifting to enhance lower bounds on delay margins, bypassing previous approximation methods.

## Key findings

- Improved lower bounds on maximum delay margin.
- Direct solution of interpolation problem using function theory.
- Enhanced bounds achieved by domain shifting.

## Abstract

We study the delay margin problem in the context of recent works by T. Qi, J. Zhu, and J. Chen, where a sufficient condition for the maximal delay margin is formulated in terms of an interpolation problem obtained after introducing a rational approximation. Instead we omit the approximation step and solve the same problem directly using techniques from function theory and analytic interpolation. Furthermore, we introduce a constant shift in the domain of the interpolation problem. In this way we are able to improve on their lower bound for the maximum delay margin.