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A multiple lyapunov function approach to stabilization of fuzzy control systems
Abstract
This paper addresses stability analysis and stabilization for Takagi-Sugeno fuzzy systems via a so-called fuzzy Lyapunov function which is a multiple Lyapunov function. The fuzzy Lyapunov function is defined by fuzzily blending quadratic Lyapunov functions. Based on the fuzzy Lyapunov function approach, we give stability conditions for open-loop fuzzy systems and stabilization conditions for closed-loop fuzzy systems. To take full advantage of a fuzzy Lyapunov function, we propose a new parallel distributed compensation (PDC) scheme that feedbacks the time derivatives of premise membership functions. The new PDC contains the ordinary PDC as a special case. A design example illustrates the utility of the fuzzy Lyapunov function approach and the new PDC stabilization method.
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Citations
Cited by
Chadli, M., & Karimi, H. R. (2013) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2012.2197215 · Cited by 388
RetractedThe 2017 IEEE International Conference on Fuzzy Systems
(2016) · IEEE Computational Intelligence Magazine · doi:10.1109/mci.2016.2545826 · Cited by 308
On the Stability of Interval Type-2 TSK Fuzzy Logic Control Systems
Biglarbegian, M., Melek, W. W., & Mendel, J. M. (2010) · IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) · doi:10.1109/tsmcb.2009.2029986 · Cited by 300
Jiang, X., Yu, F. R., Song, T., & Leung, V. C. M. (2022) · IEEE Transactions on Intelligent Transportation Systems · doi:10.1109/tits.2021.3065209 · Cited by 88
Metadata
- Authors
- Tanaka, K., Hori, T., & Wang, H. O.
- Venue
- IEEE Transactions on Fuzzy Systems
- Published
- 2003-08
- Volume
- 11
- Issue
- 4
- Pages
- 582-589
- ISSN
- 1063-6706 (ISSN-L)
- OpenAlex
- W2143142281
- Cited by
- 974
- References
- 0
- FWCI
- 34.41
- Type
- journal article
- Language
- en
- Open access
- closed
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- Tanaka, K., Hori, T., & Wang, H. O. (2003). A multiple lyapunov function approach to stabilization of fuzzy control systems. IEEE Transactions on Fuzzy Systems. https://doi.org/10.1109/tfuzz.2003.814861
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