Global Exponential Stability of Delayed Periodic Dynamical Systems

TL;DR

This paper analyzes the global exponential stability of delayed periodic dynamical systems, providing a general $L^{p}$ norm-based approach, with practical $L^{1}$ norm conditions that are easy to verify.

Contribution

It introduces a unified $L^{p}$ norm framework for stability analysis and highlights the sufficiency and practicality of $L^{1}$ norm criteria.

Findings

$L^{1}$ norm conditions are sufficient for stability

Comparison of stability criteria across different $L^{p}$ norms

Proposed general approach simplifies stability verification

Abstract

In this paper, we discuss delayed periodic dynamical systems, compare capability of criteria of global exponential stability in terms of various $L^{p}$ ($1\le p<\infty$) norms. A general approach to investigate global exponential stability in terms of various $L^{p}$ ($1\le p<\infty$) norms is given. Sufficient conditions ensuring global exponential stability are given, too. Comparisons of various stability criteria are given. More importantly, it is pointed out that sufficient conditions in terms of $L^{1}$ norm are enough and easy to implement in practice.