A vector Lyapunov function characterization of input-to-state stability with application to robust global stabilization of the chemostat

European Journal of Control

Volumn 14, Issue 1, 2008, Pages 47-61

  Karafyllis, Iasson ^a   Kravaris, Costas M ^b   Syrou, Lemonia ^b   Lyberatos, Gerasimos ^b  

^a TECHNICAL UNIVERSITY OF CRETE   (Greece)

^b UNIVERSITY OF PATRAS   (Greece)

Author keywords

Lyapunov function methods; Robust stability; Stabilization

Indexed keywords

ANAEROBIC DIGESTION; CHEMOSTATS; LYAPUNOV FUNCTIONS; ROBUSTNESS (CONTROL SYSTEMS);

ANAEROBIC DIGESTION PROCESS; EXTERNAL PERTURBATIONS; GLOBAL STABILIZATION; INPUT-TO-STATE STABILITY; LYAPUNOV FUNCTION METHOD; OPTIMAL STEADY STATE; ROBUST STABILITY; ROBUSTNESS MARGINS; STEADY-STATE CONDITION; VECTOR LYAPUNOV FUNCTIONS;

STABILIZATION;

EID: 46749148883     PISSN: 09473580     EISSN: None     Source Type: Journal    
DOI: 10.3166/ejc.14.47-61     Document Type: Article

References (26)

1. Antonelli R, Astolfi A. Nonlinear controller design for robust stabilization of continuous biological reactors. In Proc IEEE Conference on Control Applications, Anchorage, AL, September 2000.
2. Bastin G, Dochain D., On-line Estimation and Adaptive Control of Bioreactors, Elsevier, Amsterdam, 1990.
3. Dashkovskiy S. Ruffer BS, Wirth FR. An ISS small-gain theorem for general networks, Math Control Signals Syst 2007; 19: 93-122.
4. De Leenheer P, Smith HL. Feedback control for chemostat models. J Math Biol 2003; 46: 48-70.
5. Freedman Hl, So J.W.H., Waltman P. Chemostat competition with time delays. IMACS Ann. Comput. and Appl. Math., 5, 1/4 (12th IMACS World Congr Sci Com. Paris, July 1988), 1989; 171-173.
6. Gouze JL, Robledo G. Robust control for an uncertain chemostat model. Int J Robust Nonlinear Control 2006; 16(3): 133-155.
7. Graef SP, Andrews JF. Stability and control of anaerobic digestion. WPCF J 1974; 46: 667-682.
8. Harmard J, Rapaport A, Mazenc F. Output tracking of continuous bioreactors through recirculationand by-pass. Automatica 2006; 42: 1025-1032.
9. Khalil HK. Nonlinear Systems, 2nd edition, Macmillan, New York, 1996.
10. Karafyllis, I, Pepe P, Jiang Z-P. Stability results for systems described by retarded functional differential equations, math.OC/0612211, in Cornell University Library 2006 (http://www.arxiv.org).
11. Karafyllis I, Jiang Z-P. A small-gain theorem for a wide class of feedback systems with control applications, SIAM J Control Optimization 2007; 46(4): 1483-1517.
12. Maillerel L. Bernard O. A simple robust controller to stabilize and anaerobic digestion process. In Proc 8th Conference on Computer Applications in Biotechnology 2001; 213-218
13. Maillerel L. Bernard O. Steyer J.P. Robust regulation of anaerobic digestion processes. Water Science and Technology 2003; 48: 87-94.
14. Mazane F. Malisoff M. De Leenheer P. On the stability of periodic solutions in the perturbed chemostat, math.OC/0612167. in Cornell University Library 2006 (htto://www,arxuv.org).
15. Nersesov SG. Haddad WM. On the stability and control of nonlinear dynamical systems via vector Lyapunov functions. IEEE Trans Autom Control 2006;, 51(2), 203-215
16. Perrier, M. Dochain D. Evaluation of control strategies for anaerobic digestion processes. Int J Adapt Control Signal Proces 1993; 7: 309-321.
17. Pind PF, Angelidaki I, Ahring BK, Stamatelatou K. Lyberatos G. Monitoring and control of anaerobic reactors. In Biomethanation II (Ahring BK Ed.). Adv Biochem Eng Biotechnol 2003; 82: 135-182
18. Pullammanappallil P, Svoronos SA, Chynoweth DP and Lyberatos G. Expert system for control of anaerobic digesters. Biotechnol Bioeng, 98; 58: 13-22.
19. Smith H, Waltman P. The theory of the chemostat. Dynamics of Mocrobial Competition, Cambridge Studies in Mathematical Biology, 13. Cambridge University Press, Cambridge, 1995.
20. Switzenbaum MS, Giraldo-Gomez E, Hickey RF. Monitoring of the anaerobic methane fermentation process. Enzyme Microb Technol 1990; 12: 722-730.
21. Sontag ED. Smooth stabilization implies coprime factorization. IEEE Trans Autom Control 1989; 34: 432-443.
22. Sontag ED. Mathematical Control Theory. Deterministic Finite-Dimensional Systems. 2nd Edition, Springer-Verlag. New York, 1998.
23. Sontag ED, Ingalls B. A small-gain theorem with applications to input/outut systems, incremental stability, detectability, and interconnections, J Franklin Inst 2002; 339: 211-229.
24. Vorotnikov VI. Partial Stability and Control. Birkhauser, Boston, 1998.
25. Wolkowicz G, Xia H. Global asymptotic behavior of a chemostat model with discrete delays. SIAM J Appl Math 1997; 57: 1019-1043.
26. Wang L, Wolkowicz G. A delayed chemostat model with general nonmonotone response functions and differential removal rates, J Math Anal Appl 2006; 321: 452-468.