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Volumn 6, Issue 3, 2009, Pages 629-647

Feedback stabilization for a chemostat with delayed output

Author keywords

Chemostat; Control theory; Differential delay equations; Global stability

Indexed keywords

NITRATE; PHENOL;

EID: 70349640195     PISSN: 15471063     EISSN: 15510018     Source Type: Journal    
DOI: 10.3934/mbe.2009.6.629     Document Type: Article
Times cited : (11)

References (25)
  • 2
    • 0003554930 scopus 로고
    • Mathematics in Science and Engineering 6, Academic Press, New York
    • R. Bellman and K. Cooke, "Differential-Difference Equations," Mathematics in Science and Engineering 6, Academic Press, New York, 1963.
    • (1963) Differential-difference Equations
    • Bellman, R.1    Cooke, K.2
  • 4
    • 0024122883 scopus 로고
    • A method for computing the interval of delay values for which a differential-delay system is stable
    • J. Chiasson, A method for computing the interval of delay values for which a differential-delay system is stable, IEEE Trans. Automat. Contr., 33 (1988), 1176-1178.
    • (1988) IEEE Trans. Automat. Contr , vol.33 , pp. 1176-1178
    • Chiasson, J.1
  • 5
    • 0041758422 scopus 로고    scopus 로고
    • Feedback control for chemostat models
    • P. De Leenheer and H. Smith, Feedback control for chemostat models, J. Math. Biol., 46 (2003), 48-70.
    • (2003) J. Math. Biol , vol.46 , pp. 48-70
    • De Leenheer, P.1    Smith, H.2
  • 6
    • 0346548635 scopus 로고    scopus 로고
    • D. Dochain Ed, Hermes, Paris
    • D. Dochain (Ed.) "Automatique des Bioprocédés," Hermes, Paris, 2001.
    • (2001) Automatique des Bioprocédés
  • 7
  • 10
    • 84990581010 scopus 로고
    • Differential equations models of some parasitic infections: Methods for the study of asymptotic behavior
    • W. M. Hirsch, H. Hanisch and J. P. Gabriel, Differential equations models of some parasitic infections: Methods for the study of asymptotic behavior, Comm. Pure Appl. Math., XVIII (1985), 733-753.
    • (1985) Comm. Pure Appl. Math. , vol.18 , pp. 733-753
    • Hirsch, W.M.1    Hanisch, H.2    Gabriel, J.P.3
  • 11
    • 0001862504 scopus 로고
    • A unified approach to persistence
    • J. Hofbauer, A unified approach to persistence, Acta. Appl. Math., 14 (1989), 11-22.
    • (1989) Acta. Appl. Math , vol.14 , pp. 11-22
    • Hofbauer, J.1
  • 12
    • 1542296187 scopus 로고    scopus 로고
    • edition, Prentice Hall
    • H. Khalil, "Nonlinear Systems," 3rd edition, Prentice Hall, 2000.
    • (2000) rd
    • Khalil, H.1
  • 13
    • 0003743176 scopus 로고
    • Mathematics in Science and Engineering 191 Academic Press, New York
    • Y. Kuang, "Delay Differential Equations," Mathematics in Science and Engineering 191 Academic Press, New York, 1993.
    • (1993) Delay Differential Equations
    • Kuang, Y.1
  • 14
    • 2442502476 scopus 로고    scopus 로고
    • A global stability criterion for scalar functional differential equations
    • E. Liz, V. Tkachenko and S. Trofimchuk, A global stability criterion for scalar functional differential equations, SIAM J. Math. Anal., 35 (2003), 596-622.
    • (2003) SIAM J. Math. Anal. , vol.35 , pp. 596-622
    • Liz, E.1    Tkachenko, V.2    Trofimchuk, S.3
  • 15
    • 51249173595 scopus 로고
    • A multiparameter phytoplankton culture system driven by microcomputer
    • G. Malara and A. Sciandra, A multiparameter phytoplankton culture system driven by microcomputer, Applied Phycol., 3 (1991), 235-241.
    • (1991) Applied Phycol. , vol.3 , pp. 235-241
    • Malara, G.1    Sciandra, A.2
  • 17
    • 34547352375 scopus 로고    scopus 로고
    • On the stability of periodic solutions in the perturbed chemostat
    • F. Mazenc, M. MalisofT and P. De Leenheer, On the stability of periodic solutions in the perturbed chemostat, Math. Biosci. & Eng., 4 (2007), 319-338.
    • (2007) Math. Biosci. & Eng. , vol.4 , pp. 319-338
    • Mazenc, F.1    Malisoft, M.2    De Leenheer, P.3
  • 18
    • 0001555399 scopus 로고
    • Description of the chemostat
    • A. Novick and L. Szilard, Description of the chemostat, Science, 112 (1950), 715-716.
    • (1950) Science , vol.112 , pp. 715-716
    • Novick, A.1    Szilard, L.2
  • 22
    • 84942111823 scopus 로고
    • Kinetics of phenol oxidation by washed cells
    • W. Sokol and J. A. Howell, Kinetics of phenol oxidation by washed cells, Biotechnol. Bioeng., 23 (1981), 2039-2049.
    • (1981) Biotechnol. Bioeng , vol.23 , pp. 2039-2049
    • Sokol, W.1    Howell, J.A.2
  • 23
    • 33646855094 scopus 로고    scopus 로고
    • Delayed feedback control for a chemostat model
    • O. Tagashira and T. Hara, Delayed feedback control for a chemostat model, Math.Biosci., 201 (2006), 101-112.
    • (2006) Math.Biosci , vol.201 , pp. 101-112
    • Tagashira, O.1    Hara, T.2
  • 24
    • 32944459689 scopus 로고    scopus 로고
    • Experiment selection for the discrimination of semi-quantitative models of dynamical systems
    • I. Vatcheva, H. de Jong, O. Bernard and N. Mars, Experiment selection for the discrimination of semi-quantitative models of dynamical systems, Artificial Intelligence, 170 (2006), 472-506.
    • (2006) Artificial Intelligence , vol.170 , pp. 472-506
    • Vatcheva, I.1    De Jong, H.2    Bernard, O.3    Mars, N.4
  • 25
    • 0023313636 scopus 로고
    • Direct methods for TDS stability analysis
    • K. Walton and J. E. Marshall, Direct methods for TDS stability analysis, IEE Proceedings., 134 (1987), 101-107.
    • (1987) IEE Proceedings , vol.134 , pp. 101-107
    • Walton, K.1    Marshall, J.E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.