Global finite-time stabilization of planar nonlinear systems with disturbance

Asian Journal of Control

Volumn 14, Issue 3, 2012, Pages 851-858

  Li, Peng ^a   Zheng, Zhiqiang ^a  

^a NATIONAL UNIVERSITY OF DEFENSE TECHNOLOGY   (China)

Author keywords

finite time stabiliza tion; homogeneity; Planar nonlinear systems; super twisting algorithm

Indexed keywords

NONLINEAR CONTROL SYSTEMS;

ASYMPTOTICALLY STABLE; FINITE-TIME CONTROLLERS; FINITE-TIME STABILIZA-TION; GLOBAL FINITE-TIME STABILIZATIONS; HOMOGENEITY; PLANAR NONLINEAR SYSTEMS; SECOND ORDER SLIDING MODES; SUPER TWISTING ALGORITHM;

CONTINUOUS TIME SYSTEMS;

EID: 84861392044     PISSN: 15618625     EISSN: 19346093     Source Type: Journal    
DOI: 10.1002/asjc.377     Document Type: Article

References (26)

1. Choura, S., " Design of finite time settling regulators for linear systems," ASME J. Dyn. Syst. Meas. Control, Vol. 116, No. 4, pp. 602-609 (1994).
2. Athans, M., and, P. L. Falb, Optimal control: An Introduction to the Theory and its Applications, McGraw-Hill, New York, NY (1966).
3. Bhat, S., and, D. Bernstein, " Finite time stability of homogeneous systems," Proc. Am. Control Conf., Albuquerque, NM, pp. 602-609 (1997).
4. Bhat, S., and, D. Bernstein, " Continuous finite-time stabilization of the translational and rotational double integrators," IEEE Trans. Autom. Control, Vol. 43, No. 5, pp. 678-682 (1998). (Pubitemid 128736491)
5. Bhat, S., and, D. Bernstein, " Finite-time stability of continuous autonomous systems," SIAM J. Control Optim., Vol. 38, No. 3, pp. 751-766 (2000).
6. Hong, Y., Y. Yu, and, J. Huang, " Finite-time control for robot manipulators," Syst. Control Lett., Vol. 46, No. 4, pp. 243-253 (2002). (Pubitemid 34660490)
7. Moulay, E., " Stabilization via homogeneous feedback controls," Automatica, Vol. 44, No. 11, pp. 2981-2984 (2008).
8. Hong, Y., " Finite-time stabilization and stabilizability of a class of controllable systems," Syst. Control Lett., Vol. 46, No. 4, pp. 221-236 (2002).
9. Huang, X., W. Lin, and, B. Yang, " Global finite-time stabilization of a class of uncertain nonlinear systems," Automatica, Vol. 41, No. 5, pp. 881-888 (2005). (Pubitemid 40352402)
10. Zhao, W., S. Li, and, S. Fei, " Finite-time tracking control of a nonholonoic mobile robot," Asian J. Control, Vol. 11, No. 3, pp. 344-357 (2009).
11. Yu, X., Z. Man, and, Y. Wu, " Terminal sliding modes with fast transient performance," Proc. 36th IEEE Conf. Decis. Control, San Diego, CA, pp. 962-963 (1997).
12. Yu, X., and, Z. Man, " Fast terminal sliding-mode control design for nonlinear dynamical systems," IEEE Trans. Circuits Syst. I-Fundam. Theory Appl., Vol. 49, No. 2, pp. 261-264 (2002). (Pubitemid 34291480)
13. Yu, S., X. Yu, B. Shirinzadeh, and, Z. Man, " Continuous finite-time control for robotic manipulators with terminal sliding mode," Automatica, Vol. 41, No. 11, pp. 1957-1965 (2005).
14. Utkin, V. I., Sliding Modes in Control and Optimization, Springer-Verlag, Berlin, Germany (1992).
15. Levant, A., " Robust exact differentiation via sliding mode technique," Automatica, Vol. 34, No. 3, pp. 379-384 (1998). (Pubitemid 128413980)
16. Floquet, T., J. P. Barbot, and, W. Perruquetti, " Higher-order sliding mode stabilization for a class of nonholonomic perturbed systems," Automatica, Vol. 39, No. 36, pp. 1077-1083 (1998).
17. Levant, A., " Quasi-continuous high-order sliding mode controllers," IEEE Trans. Autom. Control, Vol. 50, No. 11, pp. 1812-1816 (2005). (Pubitemid 41748880)
18. Jaime, A. M., and, O. Marisol, " A Lyapunov approach to second-order sliding mode controllers and observers," Proc. 47th IEEE Conf. Decis. Control, Cancun, Mexico, pp. 962-963 (2008).
19. Huang, C., X. Peng, and, J. Wang, " Robust nonlinear PID controllers for anti-windup design of robot manipulators with an uncertain Jacobian matrix," Acta Autom. Sin., Vol. 34, No. 9, pp. 1113-1121 (2008).
20. Hughes, P. C., Spacecraft Attitude Dynamics, Wiley, New York, NY (1986).
21. Gustafsson, T., " On the design and implementation of a rotary crane controller," Eur. J. Control, Vol. 2, No. 3, pp. 166-175 (1996). (Pubitemid 126596491)
22. Haimo, V., " Finite time controllers," SIAM J. Control Optim., Vol. 24, No. 4, pp. 760-770 (1986).
23. Frye, M. T., S. Ding, C. Qian, and, S. Li, " Fast convergent observer design for output feedback stabilization of a planar vertical takeoff and landing aircraft," IET Proc. Control Theory Appl., Vol. 4, No. 4, pp. 690-700 (2010).
24. Filippov, A. F., Differential Equations with Dis-continuous Right-Hand Sides, Kluwer Academic Publishers, Dordrecht, The Netherlands (1988).
25. Khalil, H. K., Nonlinear Systems, Prentice-Hall, Upper Saddle River, NJ (2005).
26. Shtessel, Y. B., A. Shkolnikov, and, A. Levant, " Smooth second-order sliding modes: missile guidance applications," Automatica, Vol. 43, No. 8, pp. 1470-1476 (2007). (Pubitemid 47016377)