Stability analysis of delay differential equations via Semidefinite programming

TL;DR

This paper presents a method to analyze the stability of parameterized delay differential equations by converting the problem into a semi-definite programming formulation, enabling efficient computational solutions.

Contribution

It introduces a novel approach to stability analysis of DDEs using SDP after discretization, bridging differential equations with convex optimization techniques.

Findings

Stability problem reformulated as SDP

Efficient solution via interior point methods

Applicable to parameterized delay differential equations

Abstract

This paper studies the problem of stability of a parameterized delay differential equations (DDE see equation (0.1)). After discretizing the DDE (0.1), we show that the problem can be equivalently casted into a semi-definite programming (SDP) see (3.2), which can be solved efficiently through some popular algorithm, e.g., the interior point method [1].