Stabilization in a Two-Species Chemostat With Monod Growth Functions

IEEE Transactions on Automatic Control

Volumn 54, Issue 4, 2009, Pages 855-861

  Mazenc, Frédéric ^a   Malisoff, Michael ^b   Harmand, Jérôme ^c  

^a Louisiana State University ^*

^b LOUISIANA STATE UNIVERSITY   (United States)

^c LABORATOIRE DE BIOTECHNOLOGIE DE L ENVIRONNEMENT   (France)

Author keywords

Bioreactors; integral input to state stability (iISS); uncertain states

Indexed keywords

EID: 85008039448     PISSN: 00189286     EISSN: 15582523     Source Type: Journal    
DOI: 10.1109/TAC.2008.2010964     Document Type: Article

References (15)

1. D. Angeli, E. D. Sontag, and Y. Wang, “A characterization of integral input to state stability”, IEEE Trans. Automat. Control, vol. 45, no. 6, pp. 1082–1097, Jun. 2000.
2. O. Bernard and J.-L. Gouzé, “Nonlinear qualitative signal processing for biological systems: Application to the algal growth in bioreactors”, Math. Biosci., vol. 157, no. 1–2, pp. 357–372, 1999.
3. M. Chaves, “Input-to-state stability of rate-controlled biochemical networks”, SIAM J. Control Optim., vol. 44, no. 2, pp. 704–727, 2005.
4. P. De Leenheer and H. L. Smith, “Feedback control for chemostat models”, J. Math. Biol., vol. 46, no. 1, pp. 48–70, 2003.
5. J.-L. Gouzé and G. Robledo, Feedback Control for Competition Models With Different Removal Rates in the Chemostat INRIA, Sophia Antipolis, France, Rapport de Recherche 5555, Apr. 2005.
6. J.-L. Gouzé and G. Robledo, “Robust control for an uncertain chemostat model”, Int. J. Robust Nonlin. Control, vol. 16, no. 3, pp. 133–155, 2006.
7. F. Grognard, F. Mazenc, and A. Rapaport, “Polytopic Lyapunov functions for persistence analysis of competing species”, Discrete Continuous Dyn. Sys.-Ser. B, vol. 8, no. 1, pp. 73–93, Jul. 2007.
8. S. B. Hsu, “Limiting behavior for competing species”, SIAM J. Appl. Math, vol. 34, no. 4, pp. 760–763, 1978.
9. B. Li, “Asymptotic behavior of the chemostat: General responses and different removal rates”, SIAM J. Appl. Math, vol. 59, no. 2, pp. 411–422, 1999.
10. F. Mazenc, M. Malisoff, and P. De Leenheer, “On the stability of periodic solutions in the perturbed chemostat”, Math. Biosci. Eng., vol. 4, no. 2, pp. 319–338, 2007.
11. F. Mazenc, M. Malisoff, and J. Harmand, “Further results on stabilization of periodic trajectories for a chemostat with two species”, IEEE Trans. Automat. Control, Special Issue on Systems Biology, vol. 53, no. 1, pp. 66–74, Jan. 2008.
12. H. L. Smith and P. Waltman, The Theory of the Chemostat. Cambridge, U.K.: Cambridge University Press, 1995.
13. E. D. Sontag, “Smooth stabilization implies coprime factorization”, IEEE Trans. Automat. Control, vol. AC-34, no. 4, pp. 435–443, Apr. 1989.
14. E. D. Sontag, “Input-to-state stability: Basic concepts and results”, in Nonlinear and Optimal Control Theory, A. Agrachev, A. Morse, E. Sontag, H. Sussmann, and V. Utkin, Eds. Berlin, Germany: Springer-Verlag, 2008, vol. 1932, pp. 163–220.
15. G.Wolkowicz and Z. Lu, “Global dynamics of a mathematical model of competition in the chemostat: General response functions and different death rates”, SIAM J. Appl. Math, vol. 52, no. 1, pp. 222–233, 1992.