Asymptotic Stabilisation of Multiple Input Nonlinear Systems via Sliding Modes

Dynamics and Control

Volumn 8, Issue 3, 1998, Pages 231-254

  Lu, Xiao Yun ^a   Spurgeon, Sarah K ^a  

^a UNIVERSITY OF LEICESTER   (United Kingdom)

Author keywords

Asymptotic analysis; Discontinuous differential equations; Dynamic feedback control; Nonlinear systems; Sliding modes; Stabilisation; Zero dynamics

Indexed keywords

DIFFERENTIAL EQUATIONS; FEEDBACK; FEEDBACK CONTROL; NONLINEAR SYSTEMS; STABILIZATION;

ASYMPTOTIC ANALYSIS; SLIDING MODES;

CONTROL THEORY;

EID: 0032121534     PISSN: 09254668     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008206419550     Document Type: Article

References (23)

1. Aubin, J. P. and Cellina, A., Differential Inclusions, Springer-Verlag: Berlin, 1984.
2. Bartolini, G. and Zolezzi, T., "Generalised variable structure control of deterministically uncertain systems: chattering reduction and non matching uncertainties," Proc. 1st European Control Conference, Grenoble, pp. 2597-2600, 1991.
3. Cavallo, A. and De Maria, G., "Some control problems solved via a sliding manifold approach," Differential Equations and Dynamical Systems, vol. 1, pp. 295-310, 1993.
4. DeCarlo,. R. A., Zak, S. H. and Matthews, G. P., "Variable structure control of nonlinear multivariable systems: A tutorial," Proc., IEEE, vol. 76, pp. 212-232, 1988.
5. Filippov, A. F., "Differential equations with discontinuous right hand side," Amer. Math. Soc. Translations, vol. 42 ser. 2, pp. 199-231, 1964.
6. Fliess, M., "What the Kalman state variable representation is good for," in Proc. IEEE CDC, Honolulu, Hawaii, pp. 1282-1287, 1990.
7. Gopalswamy, S. and Hedrick, J. K., "Tracking nonlinear non-minimum phase systems using sliding control," Int. J. Contr., vol. 57, pp. 1141-1158, 1993.
8. Hahn, W., Stability of Motion, Springer-Verlag: New York, 1967.
9. Isidori, A., Nonlinear Control Systems, Springer-Verlag, 1989.
10. Isidori, A. and Byrnes, C. I., "Output regulation of nonlinear systems," IEEE Trans. Auto. Contr., vol. AC-35, pp. 131-140, 1990.
11. Levant, A., "Sliding order and sliding accuracy in sliding mode control," Int., J. Control, vol. 58, pp. 1247-1263, 1993.
12. Lu, X. Y. and Spurgeon, S. K., "Asymptotic feedback linearisation and control of non-flat systems via sliding modes," in Proc. of the 3rd European Control Conference, Rome, Italy, pp. 693-698, 1995.
13. Marino, R., "Static and dynamic feedback linearisation of nonlinear systems," in Perspectives in Control Theory, Proc. of the Silpia Conference, Birkhäuser, Boston, pp. 249-260, 1988.
14. Nijmeijer, H. and van der Schaft, Nonlinear Dynamical Control Systems, Springer-Verlag: New York, 1990.
15. Paden, B. E. and Sastry, S. S., "A calculus for computing Filippov's differential inclusion with application to the variable structure control of robot manipulators," IEEE Trans. Circuits and Syst., vol. CAS-34, pp. 73-82, 1987.
16. Sanderberg, Irwin W., "Global implicit function theorems," IEEE Trans. Circuits & Systems, vol. CAS-28, pp. 145-149, 1981.
17. Sira-Ramirez, H., "A dynamical variable structure control strategy in asymptotic output tracking problems," IEEE Trans. Auto. Contr., vol. AC-38, pp. 615-620, 1993.
18. Sira-Ramirez, H., "On the dynamical sliding mode control of nonlinear systems," Int. J. Control, vol. 57, pp. 1039-1061, 1993.
19. Slotine, J-J. E. and Coetsee, J. A., "Adaptive sliding controller synthesis for non-linear systems," Int. J. Control, vol. 43, pp. 1631-1651, 1986.
20. Utkin, V. I., Sliding Modes in Control and Optimisation, Springer-Verlag: Berlin, 1992.
21. van der Schaft, A. J., "Representing a nonlinear state space system as a set of higher order differential equations in the inputs and outputs," Syst. Contr. Letts., vol. 12, pp. 151-160, 1989.
22. Vidyasagar, M., "Decomposition techniques for large-scale systems with nonadditive interactions: stability and stabilisability," IEEE Trans. Auto. Contr., vol. AC-25, pp. 773-779, 1980.
23. Willems, J. L., Stability Theory of Dynamical Systems, Nelson, 1970.