Globally convergent real-time differentiation via second order sliding modes

International Journal of Systems Science

Volumn 38, Issue 10, 2007, Pages 833-844

  Pisano, Alessandro ^a   Usai, Elio ^a  

^a UNIVERSITY OF CAGLIARI   (Italy)

Author keywords

Global output feedback; Real time differentiators; Second order sliding modes

Indexed keywords

DIFFERENTIATION (CALCULUS); FEEDBACK CONTROL; GLOBAL OPTIMIZATION; PROBLEM SOLVING; REAL TIME SYSTEMS; SWITCHING FUNCTIONS;

GLOBAL CONVERGENCE PROPERTIES; GLOBAL OUTPUT-FEEDBACK; REAL-TIME DIFFERENTIATORS; SECOND-ORDER SLIDING MODES;

SLIDING MODE CONTROL;

EID: 35348866895     PISSN: 00207721     EISSN: 14645319     Source Type: Journal    
DOI: 10.1080/00207720701419834     Document Type: Article

References (17)

1. N.A. Atassi and H.K. Khalil, "A separation principle for the stabilization of a class of nonlinear systems", IEEE Trans. Automat. Contr., 44, pp. 1672-1687, 1999.
2. G. Bartolini, A. Ferrara and E. Usai, "On boundary layer reduction in sliding mode control of siso uncertain nonlinear systems", in Proceedings of the 1998 IEEE International Conference on Control Applications, Trieste, Italy, 1998, pp. 242-247.
3. G. Bartolini, A. Pisano and E. Usai, "First and second derivative estimation by sliding mode technique", J. Signal. Process., 4, pp. 167-176, 2000a.
4. G. Bartolini, A. Pisano, A. Levant and E. Usai, "On the robust stabilization of nonlinear uncertain systems with incomplete state availability", Trans. ASME, J. Dyn. Syst., Measure. Contr., 122, pp. 738-745, 2000b.
5. G. Bartolini, A. Ferrara, A. Pisano and E. Usai, "On the convergence properties of a second-order sliding mode control scheme for nonlinear uncertain systems", Int. J. Contr., 4, pp. 718-731, 2001a.
6. G. Bartolini, A. Pisano and E. Usai, "Global stabilization for nonlinear uncertain systems with unmodeled actuator dynamics", IEEE Trans. Automat. Contr., 46, pp. 1826-1832, 2001b.
7. G. Bartolini, A. Pisano and E. Usai, "An improved second-order sliding mode control scheme robust against the measurement noise", IEEE Trans. Automat. Contr., 49, pp. 1731-1737, 2004.
8. J. Davila, L. Fridman and A. Levant, "Second-order sliding-mode observer for mechanical systems", IEEE Trans. Automat. Contr., 50, pp. 1785-1789, 2005.
9. M. Fliess and S.T. Glad, "An algebraic approach to linear and nonlinear control", in Essays on Control: Perspectives in the Theory and Its Applications, H.L. Trentelman and J.C. Willems, Eds, Boston: Birkhauser, Vol. 14, 1993, pp. 223-265.
10. M. Fliess, J. Lévine, Ph. Martin and P. Rouchon, "Flatness and defect of nonlinear systems: introductory theory and examples", Int. J. Contr., 61, pp. 1327-1361, 1995.
11. A. Isidori, Non Linear Control Systems, 3rd ed., New York: Springer Verlag, 1995.
12. A. Levant, "Robust exact differentiation via sliding mode technique", Automatica, 34, pp. 379-384, 1998.
13. A. Levant, "High-order sliding modes: differentiation and output-feedback control", Int. J. Contr., 76, pp. 924-941, 2003.
14. H. Nijmeijer and I.M.Y. Mareels, "An observer look at synchronization", IEEE Trans. Circ. Syst. - I, 44, pp. 882-890, 1997.
15. V.I. Utkin, Sliding Modes in Control and Optimization, Berlin: Springer Verlag, 1992.
16. J.-X. Xu, Q.-W. Jia and T.H. Lee, "On the design of a nonlinear adaptive variable structure derivative estimator, IEEE Trans. Automat. Contr., 45, pp. 1028-1033, 2000.
17. X. Yu and J.-X. Xu, "Nonlinear derivative estimator", Electronic Lett., 32, pp. 1445-1447, 1992.