Arc-length-based Lyapunov tests for convergence and stability in systems having a continuum of equilibria

Proceedings of the American Control Conference

Volumn 4, Issue , 2003, Pages 2961-2966

  Bhat, Sanjay P ^a   Bernstein, Dennis S ^b  

^a INDIAN INSTITUTE OF TECHNOLOGY BOMBAY   (India)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; LYAPUNOV METHODS;

LYAPUNOV TESTS;

SYSTEM STABILITY;

EID: 0142184076     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (14)

1. U. Helmcke and J. B. Moore, Optimization and Dynamical Systems, Springer-Verlag, London, 1994.
2. S. L. Campbell and N. J. Rose, "Singular perturbation of autonomous linear systems," SIAM J. Math. Analysis, vol. 10, pp. 542-551, 1979.
3. D. S. Bernstein and S. P. Bhat, "Lyapunov stability, semistability, and asymptotic stability of matrix second-order systems," ASME Trans. J. Vibr. Acoustics, vol. 117, pp. 145-153, 1995.
4. S. P. Bhat and D. S. Bernstein, "Lyapunov analysis of semistability," in Amer. Contr. Conf., 1999, pp. 1608-1612.
5. S. P. Bhat and D. S. Bernstein, "Nontangency-based Lyapunov tests for convergence and stability in systems having a continuum of equilibria, " submitted to SIAM Journal of Control and Optimization, 2002.
6. M. Feinberg, "The existence and uniqueness of steady states for a class of chemical reaction networks," Arch. Rational Mech. Anal., vol. 132, pp. 311-370, 1995.
7. E. D. Sontag, "Structure and stability of certain chemical networks and applications to the kinetic proof-reading model of t-cell receptor signal transduction," IEEE Trans. Autom. Contr., vol. 46, pp. 1028-1047, 2001.
8. D. S. Bernstein and S. P. Bhat, "Nonnegativity, reducibility and semistability of mass action kinetics," in Conf. on Dec. and Contr., 1999, pp. 2206-2211.
9. J. A. Jacquez and C. P. Simon, "Qualitative theory of compartmental systems," SIAM Review, vol. 35, pp. 43-79, 1993.
10. A. Ilchmann, Non-Identifier-Based High Gain Adaptive Control, Springer, London, 1993.
11. D. R. Mudgett and A. S. Morse, "Adaptive stabilization of linear systems with unknown high-frequency gain," IEEE Trans. on Autom. Contr., vol. 30, pp. 549-554, 1985.
12. N. P. Bhatia and O. Hajek, Local Semi-Dynamical Systems, Springer-Verlag, Berlin, 1969.
13. P. Hartman, Ordinary Differential Equations, Birkhäuser, Boston, Second edition, 1982.
14. T. M. Apostol, Mathematical Analysis, Addison-Wesley, Second edition, 1974.