Positivity and Stability Analysis of Homogeneous Coupled Differential-Difference Equations With Time-Varying Delays

• 成果类型: Article
• 署名作者: Cui, Yukang; Shen, Jun; Zhang, Wei; Feng, Zhiguang; Gong, Xin
• 署名单位: Shenzhen University; Peng Cheng Laboratory; Nanjing University of Aeronautics & Astronautics; Chongqing Three Gorges University; Harbin Engineering University; Shenzhen University; University of Hong Kong
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3122380
• 发表日期: 2022
• 页码: 5493-5500
• 关键词: Delays; mathematical models; Time-varying systems; Difference equations; Stability criteria; asymptotic stability; trajectory; Coupled differential-difference equations; homogeneous systems; positive systems; systems with time-delays

摘要

This article studies the positivity and stability of homogeneous coupled differential-difference equations with time-varying delays. First, a sufficient positivity condition is proposed for the nonlinear coupled differential-difference equations with delays. Then, based on this positivity condition, we present necessary and sufficient conditions ensuring the exponential stability and bounding the decay rate for time-delay homogeneous coupled differential-difference equations with homogeneity of degree one. Furthermore, the necessary and sufficient condition is extended to the global polynomial stability analysis of homogeneous coupled differential-difference equations when the degree of homogeneity is greater than one, and the decay rate is also investigated. Two numerical examples are employed to show the effectiveness of the obtained results.