μ-Stability of Positive Homogeneous Differential-Difference Equations With Unbounded Time-Varying Delays

• 成果类型: Article
• 署名作者: Cui, Yukang; Wu, Zongze; Gong, Xin; Basin, Michael V.; Huang, Tingwen
• 署名单位: Shenzhen University; Southeast University - China; Ningbo University of Technology; Universidad Autonoma de Nuevo Leon; Shenzhen University of Advanced Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3425666
• 发表日期: 2024
• 页码: 8852-8859
• 关键词: Delays; vectors; asymptotic stability; Time-varying systems; mathematical models; STANDARDS; Thermal stability; Differential-difference equations (DDEs); mu-stability; homogeneous cooperative systems; positive systems; unbounded time-varying delays

摘要

This note studies the stability problem of nonlinear positive differential-difference equations with unbounded time-varying delays. Under assumptions on the nonlinear vector fields, such as being homogeneous, cooperative, and order-preserving, conditions are derived for positivity and asymptotic stability of nonlinear differential-difference equations, which include the corresponding linear system as a special case. This work features three main contributions: first, a necessary and sufficient positivity condition is proposed for nonlinear differential-difference equations with delays. Then, utilizing the concept of homogeneity, a necessary and sufficient condition is provided for the global asymptotic stability of such positive nonlinear systems with unbounded delays. Finally, we analyze the global mu-stability of the systems with unbounded time-varying delays to estimate the convergence rates of the system dynamics. The effectiveness of the obtained theoretical results is illustrated by numerical examples, including an analysis of nonlinear epidemic-spreading processes.