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1Controller design for TS models using delayed non-quadratic Lyapunov functions Zs. Lendek, Member, IEEE, T. M. Guerra, Member, IEEE, and J. Lauber, Abstract—In the last few years, non-quadratic Lyapunov func-tions have been more and more frequently used in the analysis and controller design for Takagi-Sugeno fuzzy models. In this paper we developed relaxed conditions for controller design using nonquadratic Lyapunov functions and delayed controllers and give a general framework for the use of such Lyapunov functions. The two controller design methods developed in this framework outperform and generalize current state-of-the-art methods. The proposed methods are extended to robust and H ∞ control and α-sample variation. Index Terms—discrete-time Takagi-Sugeno models, controller design, non-quadratic Lyapunov functions, LMI. I