A passivity-based stability criterion for a class of biochemical reaction networks
-
1.
Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY, 12180
-
2.
Department of Mathematics, Rutgers, The State University of New Jersey, Hill Center, 110 Frelinghuysen Road, Piscataway, NJ 08854
-
Received:
01 May 2007
Accepted:
29 June 2018
Published:
01 January 2008
-
-
MSC :
Primary: 34D23, 93A15,93D30; Secondary: 34D20, 05C50.
-
-
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.
Citation: Murat Arcak, Eduardo D. Sontag. A passivity-based stability criterion for a class of biochemical reaction networks[J]. Mathematical Biosciences and Engineering, 2008, 5(1): 1-19. doi: 10.3934/mbe.2008.5.1
-
Abstract
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.
-
-
-
-