Multistability in systems with counter-clockwise input-output dynamics

IEEE Transactions on Automatic Control

Volumn 52, Issue 4, 2007, Pages 596-609

  Angeli, David ^a  

^a UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Multistability; Passivity; Positive feedback interconnections

Indexed keywords

CONTROL SYSTEM ANALYSIS; CONTROL SYSTEM STABILITY; DYNAMICS; INTERCONNECTION NETWORKS;

COUNTER-CLOCKWISE INPUT-OUTPUT DYNAMICS; MULTISTABILITY; POSITIVE FEEDBACK INTERCONNECTIONS;

FEEDBACK CONTROL;

EID: 34247362889     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2007.894507     Document Type: Article

References (33)

1. D. Angeli, "Systems with counterclockwise Input-Output dynamics," IEEE Trans. Autom. Control, vol. 51, no. 7, pp. 1130-1143, Jul. 2006.
2. D. Angeli, "New analysis technique for multistability detection," IEE Proc. Syst. Biol., vol. 153, no. N. 2, pp. 61-69, 2006.
3. D. Angeli, J. Ferrell, and E. D. Sontag, "Detection of multi-stability, bifurcations, and hysteresis in a large class of biological positive-feedback systems," in Proc. Natl. Acad. Sci., 2004, vol. 101, pp. 1822-1827.
4. D. Angeli, E. D. Sontag, and Y. Wang, "A characterization of integral input-to-state stability," IEEE Trans. Autom. Control, vol. 45, no. 6, pp. 1082-1097, Jun. 2000.
5. D. Angeli and E. D. Sontag, "Multi-stability in monotone input /output systems," Syst. Control Lett., vol. 51, no. 3-4, pp. 185-202, 2004.
6. D. Angeli and E. D. Sontag, "Monotone control systems," IEEE Trans. Autom. Control, vol. 48, no. 10, pp. 1684-1699, Oct. 2003.
7. O. Cinquin and J. Demongeot, "Positive and negative feedback: Striking a balance between necessary antagonists," in J. Theoret. Biol., 2002, vol. 216, pp. 229-241.
8. M. Delbrück, "Génétique du bactériophage in unités biologiques douées de continuité génétique," in Colloques Internationaux du Centre National de la Recherche Scientifique, Paris, 1949, vol. 8, pp. 91-103.
9. M. Farkas, "Periodic motions," in Applied Mathematical Sciences Series. New York: Springer-Verlag, 1994, vol. 104.
10. H. Federer, "Geometric measure theory," in Classics in Mathematics. New York: Springer-Verlag, 1996.
11. M. Feinberg, "Multiple steady states for chemical reactions networks of deficiency one," Arch. Rational Mech. Anal., vol. 132, pp. 371-406, 1995.
12. B. Fiedler and T. Gedeon, "A Lyapunov function for tridiagonal competitive-cooperative systems," SIAM J. Math. Anal., vol. 30, no. 3, pp. 469-478, 1999.
13. T. S. Gardner, C. R. Cantor, and J. J. Collins, "Construction of a genetic toggle switch in Escherichia Coli," Nature, vol. 403, pp. 339-342, 2000.
14. R. B. Gorbet and K. A. Morris, "Generalized dissipation in hysteretic systems," in Proc. 37th IEEE Conf. Decision Control, 1998, vol. 4, pp. 4133-4138.
15. R. B. Gorbet and K. A. Morris, "Closed-loop position control of preisach hystereses," J. Intell. Mater. Smart Struct., vol. 14, no. 8, pp. 473-538, 2003.
16. J. L. Gouzé, "Positive and negative circuits in dynamical systems," J. Biol. Syst. 6, pp. 11-15, 1998.
17. C. Jeffries, V. Klee, and van den Driessche, "When is a matrix sign stable?," Can. J. Math., vol. 29, pp. 315-326, 1977.
18. A. Isidori, Nonlinear Control Systems II, Communications and Control Engineering Series. London, U.K.: Springer-Verlag, 1999.
19. T. Iwasaki and S. Hara, "Generalized KYP lemma: Unified frequency domain inequalities with design applications," IEEE Trans. Autom. Control, vol. 50, no. 1, pp. 41-59, Jan. 2005.
20. M. Laurent and N. Kellershohn, "Multistability: A major means of differentiation and evolution in biological systems," Trends Biochem. Sci., vol. 24, pp. 418-422, 1999.
21. R. de la Llave and C. E. Wayne, "On Irwin's proof of the pseudostable manifold theorem," Math. Z., vol. 219, pp. 301-321, 1995.
22. R. Lozano, B. Brogliato, O. Egeland, and B. Maschke, Dissipative Systems Analysis and Control: Theory and Applications. London, U.K.: Springer-Verlag, 2000.
23. R. Ortega, A. Loria, P. J. Nicklasson, and H. Sira-Ramirez, "Passivity-based control of Euler-Lagrange systems: Mechanical, electrical and electromechanical applications," in Communications and Control Engineering Series. New York: Springer-Verlag, 1998.
24. R. Ortega, A. van der Schaft, I. Mareels, and B. Maschke, "Putting energy back in control," IEEE Control Syst. Mag., vol. 21, no. 2, pp. 18-33, Apr. 2001.
25. R. Ortega, D. Jeltsema, and J. Scherpen, "Power shaping: A new paradigm for stabilization of nonlinear RLC circuits," IEEE Trans. Autom. Control, vol. 48, no. 10, Oct. 2003.
26. R. Sepulchre, Constructive Nonlinear Control, Communications and Control Engineering Series. New York: Springer-Verlag, 1997.
27. R. Sepulchre and G. B. Stan, "Feedback mechanisms for global oscillations in Lure systems," Syst. Control Lett., vol. 54, pp. 809-818, 2005.
28. M. Shiota, "Geometry of subanalytic and semialgebraic sets," in Progress in Mathematics. Boston, MA: Birkhäuser, 1997.
29. E.D. Sontag, Ed., Mathematical Control Theory: Deterministic Finite Dimensional Systems, ser. Texts in Applied Mathematics. New York: Springer-Verlag, 1998, vol. 6.
30. C. Soulé, "Graphic requirements for multistationarity," Complexus, vol. 1, pp. 123-133, 2003.
31. A. J. van der Schaft, L2-Gain and Passivity Techniques in Nonlinear Control, 2nd ed. London, U.K.: Springer-Verlag.
32. J. C. Willems, "Dissipative dynamical systems, part I: General theory," Arch. Rat. Mech. An., vol. 45, pp. 321-351, 1972.
33. J. C. Willems, "Dissipative dynamical systems, part II: Linear systems with quadratic supply rates," Arch. Rat. Mech An., vol. 45, pp. 352-393, 1972.