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

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 limit...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2023-09, Vol.68 (9), p.5775-5782
Main Authors: Zenati, Abdelhafid, Aouf, Nabil, Tadjine, Mohamed, Laleg-Kirati, Taous-Meriem
Format: Article
Language:English
Subjects:
Computer Science
Dynamic models
Dynamic stability
Liapunov functions
Multiagent systems
Nonlinear systems
Nonlinearity
Sequences
System theory
Systems and Control
Systems theory
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Summary: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 ([Formula Omitted]) 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.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2023.3281514