On necessary conditions for almost global stability

IEEE Transactions on Automatic Control

Volumn 48, Issue 4, 2003, Pages 631-634

  Monzon, Pablo ^a  

^a UNIVERSIDAD DE LA REPÚBLICA   (Uruguay)

Author keywords

Almost global stability; Density functions; Nonlinear systems

Indexed keywords

ASYMPTOTIC STABILITY; LYAPUNOV METHODS; NONLINEAR SYSTEMS; PROBABILITY DENSITY FUNCTION;

GLOBAL STABILITY;

SYSTEM STABILITY;

EID: 0037397496     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2003.809786     Document Type: Article

References (12)

1. A. Rantzer, "A dual to Lyapunov stability theorem," Syst. Control Lett., vol. 42, no. 3, pp. 161-168, Mar. 2001.
2. _, "A converse theorem for density functions," in Proc. IEEE Conf. Decision Control, Las Vegas, NV, Dec. 2002, pp. 1890-1891.
3. _, "Almost global stability of phased-locked loops," Lund Inst. Technol., Lund, Sweden, Tech. Rep., 2001.
4. E. Sontag, "A 'universal' construction of Artstein's theorem on nonlinear stabilization," Syst. Control Lett., vol. 13, no. 2, pp. 117-123, 1989.
5. J. Doyle, V. Nevistić, and J. Primbs, "On receding horizon extensions and control Lyapunov functions," in Proc. 1998 Amer. Control Conf., Philadelphia, PA, June 1998, pp. 117-123.
6. A. Rantzer and P. Parrilo, "On convexity in stabilization of nonlinear systems," in IEEE Conf. Decision Control, Sidney, Australia, Dec. 2000.
7. A. Rantzer and F. Ceragioli, "Smooth blending of nonlinear controllers using density functions," presented at the European Control Conf., Porto, Brazil, Sep. 2001.
8. L. Grune, E. Sontag, and F. Wirth, "Asymptotic stability equals exponential stability, and ISS equals finite energy gain - If you twist your eyes," Syst. Control Lett., vol. 38, pp. 127-134, 1999.
9. J. L. Massera, "On Liapunoff 's conditions of stability," Ann. Math., vol. 50, pp. 705-721, 1949.
10. S. Smale, "On the structure of manifolds," Amer. J. Math., vol. 84, pp. 387-399, 1962.
11. J. Milnor, Lectures on the h-Cobordism Theorem. Princeton, NJ: Princeton Univ. Press, 1965.
12. H. Khalil, Nonlinear Systems. Upper Saddle River, NJ: Prentice-Hall, 1996.