Feedback stabilization for a chemostat with delayed output
We apply basic tools of control theory toa chemostat model that describes the growth of onespecies of microorganisms that consume a limiting substrate. Under theassumption that available measurements of the model have fixed delay$\tau>0$, we design a family of feedback control laws with the objec...
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| Format: | Article |
| Language: | English |
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AIMS Press
2009-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.629 |
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| _version_ | 1832590180219879424 |
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| author | Gonzalo Robledo |
| author_facet | Gonzalo Robledo |
| author_sort | Gonzalo Robledo |
| collection | DOAJ |
| description | We apply basic tools of control theory toa chemostat model that describes the growth of onespecies of microorganisms that consume a limiting substrate. Under theassumption that available measurements of the model have fixed delay$\tau>0$, we design a family of feedback control laws with the objective of stabilizing the limiting substrate concentration in a fixedlevel. Effectiveness of this control problem is equivalent to global attractivity of a family of differential delay equations. We obtain sufficient conditions (upper bound for delay $\tau>0$ andproperties of the feedback control) ensuring global attractivity and localstability. Illustrative examples are included. |
| format | Article |
| id | doaj-art-4486c932457146f6910909bf97ae201a |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2009-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-4486c932457146f6910909bf97ae201a2025-01-24T01:59:54ZengAIMS PressMathematical Biosciences and Engineering1551-00182009-05-016362964710.3934/mbe.2009.6.629Feedback stabilization for a chemostat with delayed outputGonzalo Robledo0Faculty of Mechanical Engineering, Technion Israel Institute of Technology, Haifa, 32000We apply basic tools of control theory toa chemostat model that describes the growth of onespecies of microorganisms that consume a limiting substrate. Under theassumption that available measurements of the model have fixed delay$\tau>0$, we design a family of feedback control laws with the objective of stabilizing the limiting substrate concentration in a fixedlevel. Effectiveness of this control problem is equivalent to global attractivity of a family of differential delay equations. We obtain sufficient conditions (upper bound for delay $\tau>0$ andproperties of the feedback control) ensuring global attractivity and localstability. Illustrative examples are included.https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.629control theorychemostat.differential delay equationsglobal stability |
| spellingShingle | Gonzalo Robledo Feedback stabilization for a chemostat with delayed output Mathematical Biosciences and Engineering control theory chemostat. differential delay equations global stability |
| title | Feedback stabilization for a chemostat with delayed output |
| title_full | Feedback stabilization for a chemostat with delayed output |
| title_fullStr | Feedback stabilization for a chemostat with delayed output |
| title_full_unstemmed | Feedback stabilization for a chemostat with delayed output |
| title_short | Feedback stabilization for a chemostat with delayed output |
| title_sort | feedback stabilization for a chemostat with delayed output |
| topic | control theory chemostat. differential delay equations global stability |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.629 |
| work_keys_str_mv | AT gonzalorobledo feedbackstabilizationforachemostatwithdelayedoutput |