Sum-of-Squares Stability Analysis of Takagi-Sugeno Systems Based on Multiple Polynomial Lyapunov Functions - Université de Reims Champagne-Ardenne Access content directly
Journal Articles International Journal of Fuzzy Systems Year : 2013

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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Dates and versions

hal-01736722 , version 1 (18-10-2018)

Identifiers

  • HAL Id : hal-01736722 , version 1

Cite

Kevin Guelton, Noureddine Manamanni, Chinh-Cuong Duong, Darius L Koumba-Emianiwe. Sum-of-Squares Stability Analysis of Takagi-Sugeno Systems Based on Multiple Polynomial Lyapunov Functions. International Journal of Fuzzy Systems, 2013, 15 (1), pp.1-8. ⟨hal-01736722⟩
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