LMI relaxations for nonquadratic stabilization of discrete-time Takagi-Sugeno systems based on polynomial fuzzy Lyapunov functions

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.