The problem of state-feedback control design for discrete-time Takagi-Sugeno fuzzy systems is investigated in this paper. The strategy relies on the use of a quadratic in the state Lyapunov function that presents a homogeneous polynomial dependence of arbitrary degree g on the first instant of time of the premise variables and a multi-affine dependence on the successive instants of time of the premise variables until a maximum instant of time M. The tests cast in the form of LMI relaxations parametrized on both g and M and a feasible solution yields a non-PDC controller based on homogeneous polynomial matrices. Numerical examples show that the approach can be less conservative and more efficient than other methods available in the literature. © 2009 IEEE. 712Takagi, T., Sugeno, M., Fuzzy identification of systems and its applications to modeling and control (1985) IEEE Trans. Syst. 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