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Robust observer design for Itô stochastic time-delay systems via sliding mode control. (English) Zbl 1100.93047
Summary: This paper deals with the output feedback sliding mode control for Itô stochastic time-delay systems. The system states are unmeasured, and the uncertainties are unmatched. A sliding mode control scheme is proposed based on the state estimates. By utilizing a novel switching function, the derivative of the switching function is ensured to be finite variation. It is shown that the sliding mode in the estimation space can be attained in finite time. The sufficient condition for the asymptotic stability (in probability) of the overall closed-loop stochastic system is derived. Finally, a simulation example is shown to illustrate the proposed method.

MSC:
93E03General theory of stochastic systems
93E20Optimal stochastic control (systems)
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References:
[1] Bag, S. K.; Spurgeon, S. K.; Edwards, C.: Output feedback sliding mode design for linear uncertain systems. IEE proc. Control theory appl. 144, 209-216 (1997) · Zbl 0887.93011
[2] Chang, K. -Y.; Chang, W. -J.: Variable structure controller design with H$\infty $ norm and variance constraints for stochastic model reference systems. IEE proc. Control theory appl. 146, 511-516 (1999)
[3] Chang, K. -Y.; Wang, W. -J.: Robust covariance control for perturbed stochastic multivariable system via variable structure control. Systems control lett. 37, 323-328 (1999) · Zbl 0948.93008
[4] Choi, H. H.: A new method for variable structure control system design: a linear matrix inequality approach. Automatica 33, 2089-2092 (1997) · Zbl 0911.93022
[5] Edwards, C.; Spurgeon, S. K.: Robust output tracking using a sliding-mode controller/observer scheme. Internat. J. Control 64, 967-983 (1996) · Zbl 0858.93019
[6] 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. Automatic control 48, 2073-2074 (2003)
[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] Higham, D.: An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM rev. 43, 525-546 (2001) · Zbl 0979.65007
[9] Khasminskii, R. Z.: Stochastic stability of differential equations. (1980) · Zbl 1259.60058
[10] Lu, C. -Y.; Tsai, J. S. -H.; Jong, G. -J.; Su, T. -J.: An LMI-based approach for robust stabilization of uncertain stochastic systems with time-varying delays. IEEE trans. Automatic control 48, 286-289 (2003)
[11] Mao, X.; Koroleva, N.; Rodkina, A.: Robust stability of uncertain stochastic differential delay systems. Systems control lett. 35, 325-336 (1998) · Zbl 0909.93054
[12] Niu, Y.; Ho, D. W. C.; Lam, J.: Robust integral sliding mode control for uncertain stochastic systems with time-varying delay. Automatica 41, 873-880 (2005) · Zbl 1093.93027
[13] Niu, Y.; Lam, J.; Wang, X.; Ho, D. W. C.: Sliding mode control for nonlinear state-delayed systems using neural network approximation. IEE proc. Control theory appl. 150, 233-239 (2003)
[14] Niu, Y.; Lam, J.; Wang, X.; Ho, D. W. C.: Observer-based sliding mode control for nonlinear state-delayed systems. Internat. J. Systems sci. 35, 139-150 (2004) · Zbl 1059.93025
[15] M.C. Pai, A. Sinha, Sliding mode control of vibration in a flexible structure via estimated stated and H\infty /\mu  techniques, in: Proceedings of the American Control Conference, Chicago, IL, 2000, pp. 1118 -- 1123.
[16] Rundell, A. E.; Drakunov, S. V.; Decarlo, R. A.: A sliding mode observer and controller for stabilization of rotational motion of a vertical shaft magnetic bearing. IEEE trans. Control systems technol. 4, 598-608 (1996)
[17] Tsai, Y. -W.; Shyu, K. -K.; Chang, K. -C.: Decentralized variable structure control for mismatched uncertain large-scale systems: a new approach. Systems control lett. 43, 117-125 (2001) · Zbl 0974.93014
[18] E.I. Verriest, Stabilization of deterministic and stochastic systems with uncertain time delays, in: Proceedings of the IEEE Conference Decision and Control, Lake Buena Vista, FL, 1994, pp. 3829 -- 3834.
[19] Verriest, E. I.; Florchinger, P.: Stability of stochastic systems with uncertain time delay. Systems control lett. 24, 41-47 (1995) · Zbl 0867.34065
[20] Wang, Z.; Qiao, H.; Burnham, K. J.: On the stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters. IEEE trans. Automatic control 47, 640-646 (2002)
[21] Xu, S.; Chen, T.: Robust H$\infty $ control for uncertain stochastic systems with state delay. IEEE trans. Automatic control 47, 2089-2094 (2002)
[22] M.-S. Yang, P.-L. Liu, H.-C. Lu, Output feedback stabilization of uncertain dynamic systems with multiple state delays via sliding mode control strategy, in: ISIE’99, IEEE International Symposium on Industrial Electronics, Bled, Slovenia, 1999, pp. 1147 -- 1152.