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TECHNICAL PAPERS

Discrete Sliding Mode Control Design With Invariant Sliding Sectors

[+] Author and Article Information
Xinghuo Yu, Shuanghe Yu

Faculty of Informatics and Communication, Central Queensland University, Rockhampton, QLD 4702, Australiae-mail: {x.yu and s.yu}@cqu.edu.au

J. Dyn. Sys., Meas., Control 122(4), 776-782 (Feb 18, 2000) (7 pages) doi:10.1115/1.1318945 History: Received February 18, 2000
Copyright © 2000 by ASME
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References

Utkin, V. I., 1993, Sliding Modes in Optimization and Control, Springer-Verlag, Berlin.
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Yu,  X., 1998, “Discretization effect on a sliding mode control system with bang-bang type switching,” Int. J. Bifurcation Chaos Appl. Sci. Eng., 8, No. 6, pp. 1245–1257.
Milosavljevic,  C., 1985, “General conditions for the existence of a quasi-sliding mode on the switching hyperplane in discrete variable structure systems,” Auto. Remote Control, 46, pp. 307–314.
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Furuta, K., Pan, Y., and Hatakeyama, S., 1999, “Invariant sliding sector for variable structure control,” Proceedings of 38th IEEE Conference on Decision and Control, Phoenix AZ, Dec., pp. 5152–5157.
Yu,  X., and Potts,  R. B., 1992, “Analysis of discrete variable structure systems with pseudo sliding modes,” Int. J. Sys. Sci.,23, pp. 503–516.
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Figures

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A typical sliding sector with two linear boundaries
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A sketch map for the proof of Theorem 1
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Three regions in the phase plane
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(a) The phase plan portrait of dynamics in S1 with conjugate complex eigenvalues; (b) the phase plane portrait of dynamics in S1 with two real eigenvalues.
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Phase plane portrait in region S2
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Sketch diagram demonstrating divergence and convergence behaviors
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Trajectory with conditions (39) and (40) satisfied
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Trajectory with condition (39) violated
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Trajectory with condition (40) violated
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Trajectory with uncertainty [Δa1 Δa2]=[−0.05 0.1]

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