A passivity-based stability criterion for a class of biochemical reaction networks - Murat Arcak; Eduardo D. Sontag (Mathematical Biosciences and Engineering)
This paper presents a stability test for a class of interconnectednonlinear systems motivated by biochemical reaction networks. The mainresult determines global asymptotic stability of the network from the diag-onal stability of a dissipativity matrix which incorporates information aboutthe passivity properties of the subsystems, the interconnection structure of thenetwork, and the signs of the interconnection terms. This stability test encom-passes the secant criterion for cyclic networks presented in [1], and extends itto a general interconnection structure represented by a graph. The new stabil-ity test is illustrated on a mitogen-activated protein kinase (MAPK) cascademodel, and on a branched interconnection structure motivated by metabolicnetworks. The next problem addressed is the robustness of stability in thepresence of di®usion terms. A compartmental model is used to represent thelocalization of the reactions, and conditions are presented under which stabilityis preserved despite the di®usion terms between the compartments.