A modular condition for 2-contraction of interconnected systems
File(s)
Published version
Author(s)
Angeli, David
Martini, Davide
Innocenti, Giacomo
Tesi, Alberto
Type
Journal Article
Abstract
Despite modular conditions to guarantee stability of interconnected systems have been widely studied, few methods are available to tackle the case of systems with multiple equilibrium points. This paper introduces a modular sufficient condition for 2-contraction of nonlinear systems composed by N interconnected subsystems, on the basis of a family of upper-bounds to the L₂ gains that arise from those computed on individual input channels of a new decomposition of the variational equation associated to the 2-additive compound of the system’s Jacobian. Such a condition guarantees that this variational equation is exponentially contracting, thus preventing oscillatory behaviours and enabling convergence towards equilibria. The L₂ gains are obtained by solving suitable Linear Matrix Inequalities (LMIs) of dimension significantly lower than those concerning the original nonlinear system. Three interconnected Thomas’ systems are considered in order to illustrate the application of the modular condition and its degree of conservatism.
Date Issued
2026-07-01
Date Acceptance
2026-05-20
Citation
European Journal of Control, 2026, 90
ISSN
0947-3580
Publisher
Elsevier BV
Journal / Book Title
European Journal of Control
Volume
90
Copyright Statement
© 2026 The Author(s). Published by Elsevier Ltd on behalf of European Control Association. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
License URL
Publication Status
Published
Article Number
101533
Date Publish Online
2026-05-23