Quantization, time delays, and nonlinear stabilization

IEEE Transactions on Automatic Control

Volumn 51, Issue 7, 2006, Pages 1190-1195

  Liberzon, Daniel ^a  

^a University of Illinois at Urbana Champaign   (United States)

Author keywords

Input to state stability; Nonlinear system; Quantized control; Small gain condition; Time delays

Indexed keywords

CLOSED LOOP CONTROL SYSTEMS; DELAY CONTROL SYSTEMS; DIFFERENTIAL EQUATIONS; FEEDBACK CONTROL; ROBUSTNESS (CONTROL SYSTEMS); SYSTEM STABILITY;

DYNAMIC QUANTIZATION STRATEGY; QUANTIZED FEEDBACK CONTROL METHODOLOGY; TIME DELAYS;

NONLINEAR CONTROL SYSTEMS;

EID: 33746034150     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2006.878780     Document Type: Article

References (30)

1. D. Angeli and E. Sontag, "Forward completeness, unboundedness observability, and their Lyapunov characterizations," Syst. Control Lett., vol. 38, pp. 209-217, 1999.
2. P. Antsaklis and J. Baillieul, Eds., IEEE Trans. Autom. Control, Special Issue on Networked Control Systems, vol. 49, no. 9, Sep. 2004.
3. R. W. Brockett and D. Liberzon, "Quantized feedback stabilization of linear systems," IEEE Trans. Autom. Control, vol. 45, no. 7, pp. 1279-1289, Jul. 2000.
4. P. D. Christofides and A. R. Teel, "Singular perturbations and input-to-state stability," IEEE Trans. Autom. Control, vol. 41, no. 11, pp. 1645-1650, Nov. 1996.
5. E. Fridman, A. Seuret, and J.-P. Richard, "Robust sampled-data stabilization of linear systems: An input delay approach," Automatica, vol. 40, pp. 1441-1446, 2004.
6. K. Gu, V. L. Kharitonov, and J. Chen, Stability of Time-Delay Systems. Boston, MA: Birkhäuser, 2003.
7. J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations. New York: Springer-Verlag, 1993.
8. J. K. Hale and S. M. Verduyn Lunel, "Effects of small delays on stability and control," in Operator Theory and Analysis, Volume 122 of Operator Theory: Advances and Applications, H. Bart, I. Gohberg, and A. C. M. Ran, Eds. Basel, Germany: Birkhäuser, 2001, pp. 275-301.
9. P. F. Hokayem and M. W. Spong, "Stability of quantized and delayed bilateral teleoperators," in Proc. 45th IEEE Conf. on Decision and Control, 2006, Submitted.
10. I. Hwang, D. M. Stipanovic, and C. J. Tomlin, "Polytopic approximations of reachable sets applied to linear dynamic games and to a class of nonlinear systems," in Advances in Control, Communication Net works, and Transportation Systems: In Honor of Pravin Varaiya, Systems and Control: Foundations and Applications, E. H. Abed, Ed. Boston, MA: Birkhauser, 2005.
11. H. Ishii and B. A. Francis, "Quadratic stabilization of sampled-data systems with quantization," Automatica, vol. 39, pp. 1793-1800, 2003.
12. C.-Y. Kao and B. Lincoln, "Simple stability criteria for systems with time-varying delays," Automatica, vol. 40, pp. 1429-1434, 2004.
13. H. K. Khalil, Nonlinear Systems, 3rd ed. Upper Saddle River, NJ: Prentice-Hall, Inc., 2002.
14. A. B. Kurzhanski and P. Varaiya, "Ellipsoidal techniques for reachability analysis," in Proceedings of the 3rd International Workshop on Hybrid Systems: Computation and Control, N. Lynch and B. H. Krogh, Eds. Berlin, Germany: Springer-Velrag, 2000, vol. 1790, pp. 202-214, Lecture Notes in Computer Science.
15. D. Liberzon, "Hybrid feedback stabilization of systems with quantized signals," Automatica, vol. 39, pp. 1543-1554, 2003.
16. D. Liberzon, Switching in Systems and Control. Boston, MA: Birkhäuser, 2003.
17. D. Liberzon and J. P. Hespanha, "Stabilization of nonlinear systems with limited information feedback," IEEE Trans. Autom. Control, vol. 50, no. 6, pp. 910-915, Jun. 2005.
18. D. Nešić and D. Liberzon, "A small-gain approach to stability analysis of hybrid systems," in Proc. 44th IEEE Conf. Decision and Control, 2005, pp. 5409-5414.
19. C. De Persis, "On feedback stabilization of nonlinear systems under quantization," in Proc. 44th IEEE Conf. Decision and Control, 2005, pp. 7698-7703.
20. C. De Persis and D. Nešić, "Practical encoders for controlling nonlinear systems under communication constraints," in Proc. 44th IEEE Conf. Decision and Control, 2005, pp. 434-439.
21. B. Picasso, L. Palopoli, A. Bicchi, and K. H. Johansson, "Control of distributed embedded systems in the presence of unknown-but-bounded noise," in Proc. 43rd IEEE Conf. Decision and Control, 2004, pp. 1448-1453.
22. R. G. Sanfelice and A. R. Teel, "On hybrid controllers that induce input-to-state stability with respect to measurement noise," in Proc. 44th IEEE Conf. Decision and Control, 2005, pp. 4891-4896.
23. E. D. Sontag, "Smooth stabilization implies coprime factorization," IEEE Trans. Autom. Control, vol. 34, no. 4, pp. 435-443, Apr. 1989.
24. E. D. Sontag, "Further facts about input to state stabilization," IEEE Trans. Autom. Control, vol. 35, no. 4, pp. 473-476, Apr. 1990.
25. E. D. Sontag and Y. Wang, "On characterizations of the input-to-state stability property," Syst. Control Lett., vol. 24, pp. 351-359, 1995.
26. E. D. Sontag and Y. Wang, "New characterizations of input-to-state stability," IEEE Trans. Autom. Control, vol. 41, no. 9, pp. 1283-1294, Sep. 1996.
27. A. R. Teel, "Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem," IEEE Trans. Autom. Control, vol. 43, no. 7, pp. 960-964, Jul. 1998.
28. A. R. Teel, D. Nešić, and P. V. Kokotovic, "A note on input-to-state stability of sampled-data nonlinear systems," in Proc. 37th IEEE Conf. on Decision and Control, 1998, pp. 2473-2478.
29. Z. Wang and F. Paganini, "Global stability of nonlinear congestion control with time-delay," in Advances in Communication Control Networks, S. Tarbouriech, C. T. Abdallah, and J. Chiasson, Eds. Heidelberg, Germany: Springer-Verlag, 2004, vol. 308, pp. 199-222, Lecture Notes in Control and Information Sciences.
30. W. S. Wong and R. W. Brockett, "Systems with finite communication bandwidth constraints II: Stabilization with limited information feedback," IEEE Trans. Autom. Control, vol. 44, no. 5, pp. 1049-1053, May 1999.