A remark on multistability for monotone systems II

Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

Volumn 2005, Issue , 2005, Pages 2957-2962

  Enciso, German A ^a   Sontag, Eduardo D ^b  

^a Mathematical Biosciences Institute   (United States)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FEEDBACK CONTROL; INFORMATION ANALYSIS; MATHEMATICAL MODELS;

FEEDBACK LOOPS; MONOTONE SYSTEMS; SINGLE OUTPUT MODELS; STABILITY CRITERIUM;

ASYMPTOTIC STABILITY;

EID: 33847185557     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2005.1582614     Document Type: Conference Paper

References (14)

1. D. Angeli and E.D. Sontag. Monotone controlled systems. IEEE Trans. Autom. Control. 48:1684-1698, 2003.
2. D. Angeli and E.D. Sontag. Multistability in monotone input/output systems. Systems and Control Letters, 51:185-202, 2004.
3. D.L. DeAngelis, W.M. Post, and C.C. Travis CC. Positive Feedback in Natural Systems. Springer-Verlag, New York, 1986.
4. W. Arendt, A. Grabosch, G. Greiner, U. Groh, H.P. Lotz, U. Moustakas, R. Nagel, F. Neubrander, and U. Schlotterbeck. One-parameter Semigroups of Positive, Operators. Springer, 1980.
5. A. Berman and R.J. Plemmons. Nonnegative Matrices in the Mathematical Sciences. Academic Press, New York, 1979.
6. E. Boczko, T. Cooper, T. Gedeon, K. Mischaikow, D. Murdock, S. Pratap, and S. Wells. Structure theorems and the dynamics of nitrogen catabolite repression in yeast. Proc. Nat. Acad. Sci, 102:5647-5652, 2005.
7. P. de Leenheer and M. Malisoff. A small gain theorem for monotone systems with multi-valued input-state characteristics, to appear in the IEEE Transactions on Automatic Control, 2005.
8. G.A. Enciso and E.D. Sontag. Monotone systems under positive feedback: multistability and a reduction theorem. Systems and Control Letters, 7:34-76, 2004.
9. G.A. Enciso and E.D. Sontag. A remark on multistability for monotone systems. Proceedings of the 43rd IEEE Conference on Decision and Control (CDC), pages 249-254, 2004.
10. German A. Enciso. Monotone Input/Output Systems, and Applications to Biological Systems. PhD thesis, Rutgers University, 2005.
11. G.A. Enciso and E.D. Sontag. Multistability for monotone systems under positive feedback. manuscript in preparation, 2005.
12. M.W. Hirsch. Stability and convergence in strongly monotone dynamical systems. Reine und Angew. Math, 383:1-53, 1988.
13. M.Hirsch. Systems of differential equations that are competitive or cooperative II: convergence almost everywhere. SIAM J. Math. Anal., 16(3):423-439, 1985.
14. H.L. Smith. Monotone Dynamical Systems. AMS, Providence, RI, 1995.