Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem

IEEE Transactions on Automatic Control

Volumn 43, Issue 7, 1998, Pages 960-964

  Teel, Andrew R ^a  

^a University of California   (United States)

Author keywords

Delay systems; Functional differential equations; Input to state stability; Razumikhin theorem

Indexed keywords

DELAY CONTROL SYSTEMS; DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; FUNCTIONS; NONLINEAR CONTROL SYSTEMS; PIECEWISE LINEAR TECHNIQUES; ROBUSTNESS (CONTROL SYSTEMS);

DELAY SYSTEMS; FUNCTIONAL DIFFERENTIAL EQUATIONS; NONLINEAR SMALL GAIN THEOREM; RAZUMIKHIN THEOREM;

ASYMPTOTIC STABILITY;

EID: 0032124188     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.701099     Document Type: Article

References (20)

1. P. D. Christofides and A. R. Teel, "Singular perturbations and input-to-state stability," IEEE Trans. Automat. Contr., vol. 41, pp. 1645-1650, 1996.
2. J.-M. Coron, L. Praly, and A. R. Teel, "Feedback stabilization of nonlinear systems: Sufficient conditions and Lyapunov and input-output techniques," in Trends in Control, A. Isidori, Ed. New York: Springer-Verlag, 1995, pp. 293-347.
3. R. D. Driver, Ordinary and Delay Differential Equations. New York: Springer-Verlag, 1977.
4. T. T. Georgiou and M. C. Smith, "Robustness analysis of nonlinear feedback systems: An input-output approach," Univ. Cambridge, Tech. Rep. CUED/F-INFENG/TR 248, Mar. 1996.
5. D. P. Goodall, "Comments on a Razumikhin-type condition for feedback stabilization of uncertain dynamical time-delay systems," in Proc. European Control Conf., Rome, Italy, Sept. 1995, pp. 3342-3347.
6. J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations. New York: Springer-Verlag, 1993.
7. Z. P. Jiang, A. R. Teel, and L. Praly, "Small gain theorem for ISS systems and applications," MCSS, vol. 7, pp. 95-120, 1994.
8. H. K. Khalil, Nonlinear Systems, 2nd ed. Englewood Cliffs, NJ: Prentice Hall, 1996.
9. I. M. Y. Mareels and D. J. Hill, "Monotone stability of nonlinear feedback systems," J. Math. Syst., Est. and Contr., vol. 2, no. 3, pp. 275-291, 1992.
10. L. Praly and Z. P. Jiang, "Stabilization by output feedback for systems with ISS inverse dynamics," Syst. Contr. Lett., vol. 21, pp. 19-33, 1993.
11. M. G. Safonov, Stability and Robustness of Multivariable Feedback Systems. Cambridge, MA: MIT Press, 1980.
12. 2-boundedness of solutions of nonlinear functional equations," Bell Syst. Tech. J., vol. 43, pp. 1581-1599, 1964.
13. E. D. Sontag, "Smooth stabilization implies coprime factorization," IEEE Trans. Automat. Contr., vol. 34, pp. 435-443, 1989.
14. _, "Further facts about input to state stabilization," IEEE Trans. Automat. Contr., vol. 35, pp. 473-476, 1990.
15. E. D. Sontag and Y. Wang, "New characterizations of input to state stability," IEEE Trans. Automat. Contr., vol. 41, pp. 1283-1294, 1996.
16. _, "Detectability of nonlinear systems," in Proc. Conf. Information Sciences and Systems (CISS'96), Princeton, NJ.
17. A. R. Teel, "Additional stability results with bounded controls," in Proc. 33rd IEEE Conf. Decision and Control, Orlando, FL, 1994, pp. 133-137.
18. _, "A nonlinear small gain theorem for the analysis of control systems with saturation," IEEE Trans. Automat. Contr., vol. 41, pp. 256-270, 1996.
19. H. Trinh and M. Aldeen, "Stability robustness bounds for linear systems with delayed perturbations," IEE Proc. Control Theory Appl., July 1995, vol. 142, no. 4, pp. 345-350.
20. G. Zames, "On the input-output stability of time-varying nonlinear feedback systems - Part I: Conditions using concepts of loop gain, conicity, and positivity," IEEE Trans. Automat. Contr., vol. 11, pp. 228-238, 1966.