Abstract
This paper presents a piecewise polynomial Lyapunov function (PPLF) approach to stabilization and robust stabilization of polynomial fuzzy systems that are a generalized form of the well-known Takagi–Sugeno fuzzy systems. Both stabilization and robust stabilization conditions are formulated as sum of squares (SOS) optimization problems which can be solved by an SOS solver. A switching polynomial fuzzy controller based on switching information on the PPLF is designed to stabilize both polynomial fuzzy systems and polynomial fuzzy systems with uncertainties. In particular, by fully considering the properties of the piecewise and polynomial Lyapunov function, some relaxation are carried out in the derivation of SOS robust stabilization conditions for polynomial fuzzy systems with uncertainties. Four design examples are demonstrated to show the effectiveness of the proposed design approach in comparison with the existing approaches, i.e., linear matrix inequalities approaches and SOS stabilization and robust stabilization approaches.
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Acknowledgements
The authors would like to thank Mr. Daisuke Ogura for his contribution to this research. The first author gratefully acknowledges a scholarship for her Ph. D. study from Indonesia Endowment Fund for Education (LPDP).
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Appendix A
Appendix A
Table 4 shows the list of the shortened notations used in this paper.
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Ashar, A.U., Tanaka, M. & Tanaka, K. Stabilization and Robust Stabilization of Polynomial Fuzzy Systems: A Piecewise Polynomial Lyapunov Function Approach. Int. J. Fuzzy Syst. 20, 1423–1438 (2018). https://doi.org/10.1007/s40815-017-0435-6
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DOI: https://doi.org/10.1007/s40815-017-0435-6