The DOI matches its Crossref record; 14 of the 14 references it cites were found in a registry or an index.
Strict Lyapunov Functions for the Super-Twisting Algorithm
Abstract
A method to construct a family of strict Lyapunov functions, i.e., with negative definite derivative, for the super-twisting algorithm, without or with perturbations, is provided. This second order sliding modes algorithm is widely used to design controllers, observers and exact differentiators. The proposed Lyapunov functions ascertain finite time convergence, provide an estimate of the convergence time, and ensure the robustness of the finite-time or ultimate boundedness for a class of perturbations wider than the classical ones for this algorithm. Since the Lyapunov functions and their derivatives are quadratic forms, the operation with them is as simple as for linear time invariant systems.
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Cites
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Self-citationPrinciples of 2-sliding mode design
Levant, A. (2007) · Automatica · doi:10.1016/j.automatica.2006.10.008 · Cited by 833
Liapunov Functions and Stability in Control Theory
Bacciotti, A., & Rosier, L. (2005) · Communications and Control Engineering · doi:10.1007/b139028 · Cited by 778
Finite Time Stability and Robust Control Synthesis of Uncertain Switched Systems
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Cited by
Stability notions and Lyapunov functions for sliding mode control systems
Polyakov, A., & Fridman, L. (2014) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2014.01.002 · Cited by 420
A Robust Observer-Based Sensor Fault-Tolerant Control for PMSM in Electric Vehicles
Kommuri, S. K., Defoort, M., Karimi, H. R., & Veluvolu, K. C. (2016) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2016.2590993 · Cited by 408
Second-Order Sliding Mode Control for Nonlinear Uncertain Systems Bounded by Positive Functions
Ding, S., Wang, J., & Zheng, W. X. (2015) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2015.2448064 · Cited by 162
Robust Sensors-Fault-Tolerance With Sliding Mode Estimation and Control for PMSM Drives
Kommuri, S. K., Lee, S. B., & Veluvolu, K. C. (2018) · IEEE/ASME Transactions on Mechatronics · doi:10.1109/tmech.2017.2783888 · Cited by 140
Coutinho, D., Vargas, A., Feudjio, C., Benavides, M., & Wouwer, A. V. (2019) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2018.07.006 · Cited by 19
Metadata
- Authors
- Moreno, J. A., & Osorio, M.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2012-04
- Volume
- 57
- Issue
- 4
- Pages
- 1035-1040
- ISSN
- 0018-9286 (ISSN-L)
- 1558-2523
- OpenAlex
- W2031945217
- Cited by
- 1,377
- References
- 14
- FWCI
- 69.54
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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