Paper Info
Title
A passivity-based stability criterion for a class of interconnected systems and applications to biochemical reaction networks
Abstract
This paper presents a stability test for a class of interconnected nonlinear systems motivated by biochemical reaction networks. One of the main results determines global asymptotic stability of the network from the diagonal 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 encompasses the "secant criterion" for cyclic networks presented in our previous paper, and extends it to a general interconnection structure represented by a graph. A second main result allows one to accommodate state products. This extension makes the new stability criterion applicable to a broader class of models, even in the case of cyclic systems. The new stability test 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 presence of diffusion terms in a compartmental system made out of identical systems.
Year
DOI
Venue
2007
10.1109/CDC.2007.4434115
New Orleans, LA
Keywords
Field
DocType
asymptotic stability,biochemistry,cascade control,graph theory,interconnected systems,matrix algebra,nonlinear control systems,biochemical reaction networks,branched interconnection structure,cyclic networks,diagonal stability,dissipativity matrix,global asymptotic stability,graph,interconnected nonlinear systems,metabolic networks,mitogen activated protein kinase cascade model,passivity-based stability criterion,secant criterion,stability testing
Graph theory,Diagonal,Passivity,Stability criterion,Mathematical optimization,Nonlinear system,Computer science,Matrix (mathematics),Control theory,Exponential stability,Interconnection
Conference
ISSN
ISBN
Citations 
0191-2216 E-ISBN : 978-1-4244-1498-7
978-1-4244-1498-7
17
PageRank 
References 
Authors
1.59
6
2
Name
Order
Citations
PageRank
murat arcak11855195.31
Eduardo D. Sontag23134781.88