Homogeneous observers, iterative design, and global stabilization of high-order nonlinear systems by smooth output feedback

IEEE Transactions on Automatic Control

Volumn 49, Issue 7, 2004, Pages 1069-1080

  Yang, Bo ^a   Lin, Wei ^a  

^a IEEE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; CLOSED LOOP CONTROL SYSTEMS; COMPUTER SIMULATION; CONTROLLABILITY; EQUIVALENCE CLASSES; FEEDBACK CONTROL; ITERATIVE METHODS; LINEAR SYSTEMS; LINEARIZATION; LYAPUNOV METHODS; OBSERVABILITY; STATE FEEDBACK;

GLOBAL ASYMPTOTIC STABILIZATION; HIGH ORDER NONLINEAR SYSTEMS; HOMOGENEOUS OBSERVERS; JACOBIAN LINEARIZATION; NONSEPARATION PRINCIPLE BASED DESIGN; SMOOTH OUTPUT FEEDBACK;

NONLINEAR CONTROL SYSTEMS;

EID: 3843064546     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2004.831186     Document Type: Article

References (29)

1. A. Bacciotti, Local Stabilizability of Nonlinear Control Systems. Singapore: World Scientific, 1992.
2. C. I. Byrnes and A. Isidori, "New results and examplse in nonlinear feedback stabilization," Syst. Control Lett., vol. 12, pp. 437-442, 1989.
3. D. Cheng and W. Lin, "On ρ - normal forms of nonlinear systems," IEEE Trans. Automat. Contr., vol. 48, pp. 1242-1248, July 2003.
4. P. E. Crouch and M. Irving, "On sufficient conditions for local asymptotic stability of nonlinear systems whose linearization is uncontrollable," Univ. Warwick, Coventry, U.K., Control Theory Centre Rep. 114, 1983.
5. W. P. Dayawansa, "Recent advances in the stabilization problem for low dimensional systems," in Proc. 2nd IFAC Symp. Nonlinear Control Systems Design, Bordeaux, France, 1992, pp. 1-8.
6. W. P. Dayawansa, C. F. Martin, and G. Knowles, "Asymptotic stabilization of a class of smooth two dimensional systems," SIAM J. Control Optim., vol. 28, pp. 1321-1349, 1990.
7. W. P. Dayawansa, private communication, 2002.
8. W. Hahn, Stability of Motion. New York: Springer-Verlag, 1967.
9. H. Hermes, "Homogeneous coordinates and continuous asymptotically stabilizing feedback controls," in Differential Equations Stability and Control, S. Elaydi, Ed. New York: Marcel Dekker, 1991, vol. 109, pp. 249-260.
10. H. Hermes, "Nilpotent and high-order approximations of vector field systems," SIAM Rev., vol. 33, pp. 238-264, 1991.
11. J. P. Gauthier, H. Hammouri, and S. Othman, "A simple observer for nonlinear systems, applications to bioreactocrs," IEEE Trans. Automat. Contr., vol. 37, pp. 875-880, July 1992.
12. A. Isidori, Nonlinear Control Systems II. New York: Springer-Verlag, 1999.
13. A. Isidori, "A tool for semiglobal stabilization of uncertain nonminimumphase nonlinear systems via, output feedback," IEEE Trans. Automat. Contr., vol. 45, pp. 1817-1827, Nov. 2000.
14. M. Kawski, "Stabilization of nonlinear systems in the plane," Syst. Control Lett., vol. 12, pp. 169-175, 1989.
15. M. Kawski, "Homogeneous stabilizing feedback laws," Control Theory Adv. Technol., vol. 6, pp. 497-516, 1990.
16. H. K. Khalil and A. Saberi, "Adaptive stabilization of a class of nonlinear systems using high-gain feedback," IEEE Trans. Automat. Contr., vol. AC-38, pp. 1031-1035, Sept. 1987.
17. A. J. Krener and A. Isidori, "Linearization by output injection and nonlinear observer," Syst. Control Lett., vol. 3, pp. 47-52, 1983.
18. A. J. Krener and M. Xiao, "Observers for linearly unobservable nonlinear systems," Syst. Control Lett., vol. 46, pp. 281-288, 2002.
19. A. J. Krener and W. Kang, "Locally convergent nonlinear observers," SIAM J. Control Optim., vol. 42, no. 1, pp. 155-177, 2003.
20. W. Lin and C. Qian, "Adding one power integrator: A tool for global stabilization of high-order lower-triangular systems," Syst. Control Lett., vol. 39, pp. 339-351, 2000.
21. W. Lin and C. Qian, "Robust regulation of a chain of power integrators perturbed by a lower-triangular vector field," Int. J. Robust Nonlinear Control, vol. 10, pp. 397-421, 2000.
22. C. Qian and W. Lin, "Output feedback control of a class of nonlinear systems: A nonseparation principle diagram," IEEE Trans. Automat. Contr., vol. 47, pp. 1710-1715, Oct. 2002.
23. C. Qian and W. Lin, "Smooth output feedback stabilization of planar systems without controllable/observable linearization," IEEE Trans. Automat. Contr., vol. 47, pp. 2068-2073, Dec. 2002.
24. C. Qian and W. Lin, "Nonsmooth output feedback stabilization of a class of genuinely nonlinear systems in the plane," IEEE Trans. Automat. Contr., vol. 48, pp. 1824-1829, Oct. 2003.
25. C. Qian and W. Lin, "A continuous feedback approach to global strong stabilization of nonlinear systems," IEEE Trans. Automat. Contr., vol. 46, pp. 1061-1079, July 2001.
26. L. Rosier, "Homogeneous Lyapunov function for homogeneous continuous vector field," Syst. Control Lett., vol. 19, pp. 467-473, 1992.
27. C. Rui, M. Reyhanoglu, I. Kolmanovsky, S. Cho, and N. H. McClamroch, "Nonsmooth stabilization of an underactuated unstable two degrees of freedom mechanical system," in Proc. 36th IEEE Conf. Decision Control, San Diego, CA, 1997, pp. 3998-4003.
28. B. Yang and W. Lin, "Output feedback stabilization of a class of homogeneous and high-order nonlinear systems," in Proc. 42nd IEEE Conf. Decision Control, Maui, HI, 2003, pp. 37-42.
29. C. Qian and W. Lin, "New results on nonsmooth output feedback stabilization of nonlinear systems," in Symposium on New Directions in Control Theory and Applications, W. Dayawansa et al., Ed. New York: Springer-Verlag, 2004.