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This paper presents a stability test for a class of interconnected nonlinearsystems motivated by biochemical reaction networks. One of the main resultsdetermines global asymptotic stability of the network from the diagonalstability of a "dissipativity matrix" which incorporates information about thepassivity properties of the subsystems, the interconnection structure of thenetwork, and the signs of the interconnection terms. This stability testencompasses the "secant criterion" for cyclic networks presented in ourprevious paper, and extends it to a general interconnection structurerepresented by a graph. A second main result allows one to accommodate stateproducts. This extension makes the new stability criterion applicable to abroader class of models, even in the case of cyclic systems. The new stabilitytest is illustrated on a mitogen activated protein kinase (MAPK) cascade model,and on a branched interconnection structure motivated by metabolic networks.Finally, another result addresses the robustness of stability in the presenceof diffusion terms in a compartmental system made out of identical systems.

A passivity-based stability criterion for a class of interconnected systems and applications to biochemical reaction networks