A passivity-based stability criterion for a class of biochemical reaction networks
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 passivit...
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| Format: | Article |
| Language: | English |
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AIMS Press
2007-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.1 |
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| author | Murat Arcak Eduardo D. Sontag |
| author_facet | Murat Arcak Eduardo D. Sontag |
| author_sort | Murat Arcak |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-49d9d9c4267849c3b21bcf918d7eb0ac |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2007-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-49d9d9c4267849c3b21bcf918d7eb0ac2025-01-24T01:57:50ZengAIMS PressMathematical Biosciences and Engineering1551-00182007-12-015111910.3934/mbe.2008.5.1A passivity-based stability criterion for a class of biochemical reaction networksMurat Arcak0Eduardo D. Sontag1Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY, 12180Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY, 12180This 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.https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.1lyapunov stabilitybiochemicalreaction networkslarge-scale systems.global stability |
| spellingShingle | Murat Arcak Eduardo D. Sontag A passivity-based stability criterion for a class of biochemical reaction networks Mathematical Biosciences and Engineering lyapunov stability biochemicalreaction networks large-scale systems. global stability |
| title | A passivity-based stability criterion for a class of biochemical reaction networks |
| title_full | A passivity-based stability criterion for a class of biochemical reaction networks |
| title_fullStr | A passivity-based stability criterion for a class of biochemical reaction networks |
| title_full_unstemmed | A passivity-based stability criterion for a class of biochemical reaction networks |
| title_short | A passivity-based stability criterion for a class of biochemical reaction networks |
| title_sort | passivity based stability criterion for a class of biochemical reaction networks |
| topic | lyapunov stability biochemicalreaction networks large-scale systems. global stability |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.1 |
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