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Rapport Année : 2023

Global Uniform Ultimate Boundedness of Semi-Passive Systems Interconnected over Directed Graphs

Anes Lazri
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Elena Panteley
Antonio Loria

Résumé

We analyse the solutions of networked heterogeneous nonlinear systems 1 ẋi = fi(xi) + ui xi ∈ R, i ∈ {1, 2, • • • , n}, (1) where fi : R → R is continuous for all i ∈ {1, 2, • • • , n} and the control inputs are set to ui := −γ n i=1 where γ > 0 is a coupling gain and aij ≥ 0 are interconnection weights. We assume that the closed-loop interconnected systems form a network with an underlying connected directed graph that contains a directed spanning tree. For these systems, we establish global uniform ultimate boundedness of the solutions, under the assumption that each system (1) defines a semi-passive [5] map ui 7 → xi. As a corollary, we also establish global uniform global boundedness of the solutions.
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hal-04298308 , version 1 (21-11-2023)

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Anes Lazri, Mohamed Maghenem, Elena Panteley, Antonio Loria. Global Uniform Ultimate Boundedness of Semi-Passive Systems Interconnected over Directed Graphs. CNRS - Laboratoire des signaux et systèmes; CNRS - GIPSA-Lab. 2023, 9 p. ⟨hal-04298308⟩
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