The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Reaching Time Estimation for “Super-Twisting” Second Order Sliding Mode Controller via Lyapunov Function Designing
Abstract
A method of a Lyapunov functions design based on resolving of the first-order partial differential equation of a special type is presented. A successful resolution of this equation guaranties a finite-time convergence for the corresponding dynamics given by an ordinary differential equation with a discontinuous right-hand side. It is also provides an analytical formula for an upper bound of the corresponding reaching time. The suggested method is applied to the problem of a stability analysis and a reaching time estimation of the, so-called, ldquosuper-twistingrdquo controller. The estimation accuracy is confirmed by numerical example.
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Citations
Cites
Differential Equations with Discontinuous Righthand Sides
Filippov, A. F. (1988) · Mathematics and Its Applications · doi:10.1007/978-94-015-7793-9 · Cited by 4,720
Cited by
Strict Lyapunov Functions for the Super-Twisting Algorithm
Moreno, J. A., & Osorio, M. (2012) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2012.2186179 · Cited by 1,377
Uniform Robust Exact Differentiator
Cruz-Zavala, E., Moreno, J. A., & Fridman, L. M. (2011) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2011.2160030 · Cited by 559
Chalanga, A., Kamal, S., Fridman, L. M., Bandyopadhyay, B., & Moreno, J. A. (2016) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2016.2523913 · Cited by 549
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
Self-citationMicroscale Precision Control of a Computer-Assisted Transoral Laser Microsurgery System
Lee, J., Deshpande, N., Caldwell, D. G., & Mattos, L. S. (2020) · IEEE/ASME Transactions on Mechatronics · doi:10.1109/tmech.2020.2973381 · Cited by 26
Metadata
- Authors
- Polyakov, A., & Poznyak, A.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2009-08
- Volume
- 54
- Issue
- 8
- Pages
- 1951-1955
- ISSN
- 0018-9286 (ISSN-L)
- 1558-2523
- OpenAlex
- W2164812525
- Cited by
- 281
- References
- 1
- FWCI
- 19.50
- Type
- journal article
- Language
- en
- Open access
- closed
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- Polyakov, A., & Poznyak, A. (2009). Reaching Time Estimation for “Super-Twisting” Second Order Sliding Mode Controller via Lyapunov Function Designing. IEEE Transactions on Automatic Control. https://doi.org/10.1109/tac.2009.2023781
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