article · IEEE Transactions on Automatic Control · 2007

Euler's Discretization of Single Input Sliding-Mode Control Systems

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Abstract

In this note, the dynamical behaviors of Euler's discretization of the equivalent control based sliding-mode control (SMC) systems are studied. We show that if the discretized SMC system is asymptotically stable, then every trajectory converges to a period-2 cycle. Bounds for the steady states are derived, which allow one to estimate the maximum chattering amplitude for a given value of the time step. The analysis and results are verified with several computer simulations.

Cite this paper

APA 7

Galias, Z., & Yu, X. (2007). Euler's Discretization of Single Input Sliding-Mode Control Systems. IEEE Transactions on Automatic Control, 52(9), 1726–1730. https://doi.org/10.1109/tac.2007.904289

MLA 9

Galias, Zbigniew, and Xinghuo Yu. “Euler's Discretization of Single Input Sliding-Mode Control Systems.” IEEE Transactions on Automatic Control, vol. 52, no. 9, 2007, pp. 1726–30, https://doi.org/10.1109/tac.2007.904289.

Chicago

Galias, Zbigniew, and Xinghuo Yu. 2007. “Euler's Discretization of Single Input Sliding-Mode Control Systems.” IEEE Transactions on Automatic Control 52 (9): 1726–30. https://doi.org/10.1109/tac.2007.904289.

Harvard

Galias, Z. and Yu, X. (2007) ‘Euler's Discretization of Single Input Sliding-Mode Control Systems’, IEEE Transactions on Automatic Control, 52(9), pp. 1726–1730. Available at: https://doi.org/10.1109/tac.2007.904289.

BibTeX

@article{galias2007euler,
  title = {{Euler's Discretization of Single Input Sliding-Mode Control Systems}},
  author = {Galias, Zbigniew and Yu, Xinghuo},
  journal = {IEEE Transactions on Automatic Control},
  volume = {52},
  number = {9},
  pages = {1726--1730},
  year = {2007},
  doi = {10.1109/tac.2007.904289}
}

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