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Global sliding mode control and application in chaotic systems. (English) Zbl 1170.93320

Summary: This paper is concerned with the stabilization problem for a class of nonlinear systems. Using the global sliding mode control approach, a novel robust control law is established to make the state of system stable and to improve the robustness and the stability of system. A new reaching law is introduced to reduce the chattering. Finally, the method is applied to chaotic systems and an example of the chaotic system is given to illustrate the advantage of the proposed method.

MSC:

93B12 Variable structure systems
93B40 Computational methods in systems theory (MSC2010)
93C10 Nonlinear systems in control theory
93B35 Sensitivity (robustness)
93C15 Control/observation systems governed by ordinary differential equations
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[1] Stipanovic, D.M., Siljak, D.D.: Robust stability and stabilization of discrete-time nonlinear systems. Int. J. Control 74, 873–879 (2001) · Zbl 1022.93034
[2] Sun, J., Liu, G.P.: State feedback and output feedback control of a class of nonlinear systems with delayed measurements. Nonlinear Anal. 67, 1623–1636 (2007) · Zbl 1123.34064
[3] Nguang, S.K.: Robust nonlinear H output feedback control. IEEE Trans. Automat. Contr. 41, 1003–1007 (1996) · Zbl 0875.93106
[4] Daniel, W.C.H., Lu, G.: Robust stabilization for a class of discrete-time nonlinear systems via output feedback: The united LMI approach. Int. J. Control 76, 105–115 (2003) · Zbl 1026.93048
[5] Hung, J.Y., Gao, W., Hung, J.C.: Variable structure control: a survey. IEEE Trans. Ind. Electron. 40, 2–22 (1993)
[6] Slotine, J.E., Li, W.: Applied Nonlinear Control. Prentice Hall, New York (1991) · Zbl 0753.93036
[7] Hung, L.C., Chung, H.Y.: Decoupled control using neural network-based sliding-mode controller for nonlinear systems. Expert Syst. Appl. 32, 1168–1182 (2007)
[8] Coradini, M.L., Orlando, G.: Linear unstable plants with saturating actuators: Robust stabilization by a time varying sliding surface. Automatica 43, 88–94 (2007) · Zbl 1140.93467
[9] Niu, Y., Daniel, W.C.H., Wang, X.: Sliding mode control for Ito stochastic systems with Markovian switching. Automatica 43, 1784–1790 (2007) · Zbl 1119.93063
[10] Wu, T.Z., Wang, J.D., Juang, Y.T.: Decoupled integral variable structure control for MIMO systems. J. Franklin Inst. 344, 1006–1020 (2007) · Zbl 1128.93013
[11] Nazzal, J.M., Natsheh, A.N.: Chaos control using sliding mode theory. Chaos Solitons Fractals 33, 695–702 (2007)
[12] Yau, H.T.: Design of adaptive sliding mode controller for chaos synchronization with uncertainties. Chaos Solitons Fractals 22, 341–347 (2004) · Zbl 1060.93536
[13] Chang, J.F., Hung, M.L., Yang, Y.S., Liao, T.L., Yan, J.J.: Controlling chaos of the family of Rossler systems using sliding mode control. Chaos Solitons Fractals 37, 609–622 (2008) · Zbl 1139.93025
[14] Chiang, T.Y., Hung, M.L., Yan, J.J., Yang, Y.S., Chang, J.F.: Sliding mode control for uncertain unified chaotic systems with input nonlinearity. Chaos Solitons Fractals 34, 437–442 (2007) · Zbl 1134.93405
[15] Wang, H., Han, Z., Xie, Q., Zhang, W.: Sliding mode control for chaotic systems based on LMI. Commun. Nonlinear Sci. Simul. (2008). doi: 10.1016/j.cnsns.2007.12.006 · Zbl 1221.93049
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