×

Sliding mode variable structure control for parameter uncertain stochastic systems with time-varying delay. (English) Zbl 1162.93014

Summary: The variable structure control problem for a class of uncertain stochastic system with time-varying delay is investigated. Firstly, a new concept of the subordinated reachability of the sliding motion is introduced to approach approximately the specified sliding surface. The variable structure control law is then proposed to ensure that the sliding motion is subordinated reachable. Furthermore, a sufficient condition for mean-square asymptotical stability of the sliding motion is given. Finally, a numerical example is presented to demonstrate the effectiveness of the obtained results.

MSC:

93B12 Variable structure systems
93E03 Stochastic systems in control theory (general)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Emelyanov, S. V., Variable Structure Control Systems (1967), Nauka: Nauka Moscow, (in Russian) · Zbl 0217.58102
[2] Utkin, V. I., Variable structure control systems with sliding modes, IEEE Trans. Automat. Control, 22 (1977)
[3] Orlov, V.; Utkin, V. I., Sliding mode control in indefinite dimensional systems, Automatica, 23, 753-757 (1987) · Zbl 0661.93036
[4] Vang, Z.; Huang, B.; Unbehauen, H., Robust reliable control for a class of uncertain nonlinear sate-delayed systems, Automatica, 35, 955-963 (1999) · Zbl 0945.93605
[5] Chen, M. L.; Tao, C. V.; Lee, T. T., Sliding mode controller for linear systems with mismatched time-varying uncertainties, J. Franklin Inst., 37, 105-115 (2000) · Zbl 0981.93012
[6] Li, X.; Decarlo, R. A., Robust sliding mode control of uncertain time-delay systems, Internat. J. Control, 76, 1296-1305 (2001) · Zbl 1036.93005
[7] Gouaisbaut, F.; Dambrine, M.; Richard, J. P., Robust control of delay systems: A sliding mode control design via LMI, Systems Control Lett., 46, 219-230 (2002) · Zbl 0994.93004
[8] Tan, C. P.; Edwards, C., An LMI approach for designing sliding mode observers, Internat. J. Control, 74, 1559-1568 (2001) · Zbl 1101.93304
[9] Xia, Y. Q.; Jia, Y. M., Robust sliding-mode control for uncertain time-delay systems: An LMI approach, IEEE Trans. Automat. Control, 48, 1086-1092 (2003) · Zbl 1364.93608
[10] Liu, Y. Q.; Deng, F. Q., The Variable Structure Control of Stochastic System (1998), South China Universary of Technology: South China Universary of Technology Guangzhou
[11] Koan, Y. C.; Wen, J. W., Robust covariance control for perturbed stochastic multivariable system via variable structure control, Systems Control Lett., 37, 323-328 (1999) · Zbl 0948.93008
[12] Niu, Yugang; Ho, Daniel W. C.; Lam, James, Robust integral sliding mode control for uncertain stochastic systems with time-varying delay, Automatica, 41, 873-880 (2005) · Zbl 1093.93027
[13] K.Y. Chang, W.J. Chang, Covariance assignment for stochastic model reference systems via sliding mode control concept, in: Proceedings of the American Control Conference, Philadelphia, PA, USA, 1998, pp. 289-292; K.Y. Chang, W.J. Chang, Covariance assignment for stochastic model reference systems via sliding mode control concept, in: Proceedings of the American Control Conference, Philadelphia, PA, USA, 1998, pp. 289-292
[14] Wang, Z.; Qiao, H.; Burnham, K. J., On the stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters, IEEE Trans. Automat. Control, 47, 640-647 (2002) · Zbl 1364.93672
[15] Niu, Yugang; Ho, Daniel W. C., Robust observer design for Itô stochastic time-delay systems via sliding mode control, Systems Control Lett., 55, 781-793 (2006) · Zbl 1100.93047
[16] Mao, X.; Koroleva, N.; Rodkina, A., Robust stability of uncertain stochastic differential delay systems, Systems Control Lett., 35, 325-336 (1998) · Zbl 0909.93054
[17] Gao, H.; Wang, C.; Zhao, L., Comments on “An LMI-based approach for robust stabilization of uncertain stochastic systems with time-varying delays”, IEEE Trans. Automat. Control, 48, 2071-2074 (2003)
[18] Verriest, E. I.; Florchinger, P., Stability of stochastic systems with uncertain time delay, Systems Control Lett., 24, 41-47 (1995) · Zbl 0867.34065
[19] Xu, S.; Chen, T., Robust H control for uncertain stochastic systems with state delay, IEEE Trans. Automat. Control, 47, 2089-2094 (2002) · Zbl 1364.93755
[20] Arnold, L., Stochastic Differential Equation: Theory and Applications (1974), John Wiley and Sons: John Wiley and Sons New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.