A passivity-based stability criterion for a class of biochemical reaction networks

This paper presents a stability test for a class of interconnected nonlinear systems motivated by biochemical reaction networks. The main result determines global asymptotic stability of the network from the diag- onal stability of a dissipativity matrix which incorporates information about the passivity properties of the subsystems, the interconnection structure of the network, and the signs of the interconnection terms. This stability test encom- passes the secant criterion for cyclic networks presented in [1], and extends it to a general interconnection structure represented by a graph. The new stabil- ity test is illustrated on a mitogen-activated protein kinase (MAPK) cascade model, and on a branched interconnection structure motivated by metabolic networks. The next problem addressed is the robustness of stability in the presence of di®usion terms. A compartmental model is used to represent the localization of the reactions, and conditions are presented under which stability is preserved despite the di®usion terms between the compartments.