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.

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.