Sum-of-Squares Stability Analysis of Takagi-Sugeno Systems Based on Multiple Polynomial Lyapunov Functions

Abstract : In this paper, another step on relaxation for Ta-kagi-Sugeno systems' stability analysis is addressed. Inspired from non-quadratic Lyapunov functions (NQLF), regarding to quadratic ones, a multiple polynomial Lyapunov function (MPLF) is proposed as an extension to polynomial Lyapunov function approaches. Following the latter post-LMI challenge, the obtained stability conditions are written in terms of a sum-of-squares (SOS) optimization problem. The proposed MPLF includes the well-studied NQLF ones as a special case. Moreover, the proposed SOS based stability conditions don't require unknown parameters in advance, as well as guarantee, when a solution exists, global stability. Therefore, these drawbacks of classical LMI based non-quadratic approaches are overcame.
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https://hal.univ-reims.fr/hal-01736722
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Submitted on : Thursday, October 18, 2018 - 4:16:11 PM
Last modification on : Wednesday, April 3, 2019 - 2:16:05 PM

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Kevin Guelton, Noureddine Manamanni, Chinh-Cuong Duong, Darius Koumba-Emianiwe. Sum-of-Squares Stability Analysis of Takagi-Sugeno Systems Based on Multiple Polynomial Lyapunov Functions. International Journal of Fuzzy Systems, Taiwan Fuzzy Systems Association, 2013, 15 (1), pp.1-8. ⟨http://www.ijfs.org.tw/ePublication/ePublication.html⟩. ⟨hal-01736722⟩

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