On the Admissibility and Stability of Multiagent Nonlinear Interconnected Positive Systems With Heterogeneous Delays

• 成果类型: Article
• 署名作者: Zenati, Abdelhafid; Aouf, Nabil; Tadjine, Mohamed; Laleg-Kirati, Taous-Meriem
• 署名单位: City St Georges, University of London; King Abdullah University of Science & Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3281514
• 发表日期: 2023
• 页码: 5775-5782
• 关键词: Delays; Interconnected systems; asymptotic stability; Stability criteria; Lyapunov methods; Eigenvalues and eigenfunctions; Urban areas; Admissibility; DELAYS; interconnected system; Lyapunov function; Nonlinear systems; positive systems; STABILITY

摘要

Many multiagent interconnected systems include typical nonlinearities, which are highly sensitive to inevitable communication delays. This makes their analysis challenging and the generalization of results from linear interconnected systems theory to those nonlinear interconnected systems very limited. This article deals with the analysis of multiagent nonlinear interconnected positive systems (MANIPS). The main contributions of this work are twofold. Based on Perron-Frobenius theorem, we first study the admissibility property for MANIPS and show that it is a fundamental requirement for this category of systems. Then, using admissibility/positivity properties and sequences of functions theory, we propose a suitable Lyapunov function candidate to conduct the analysis of the dynamical behavior of such systems. We show that the stability of MANIPS is reduced to the positiveness property (i.e., negative or positive definiteness) of a new specific matrix-valued function (Z) that we derive in this article. Furthermore, the obtained results generalize the existing theory. The quality of the results achieved is demonstrated through the applications of the developed theory on cells with a multistage maturation process dynamical models.