Nonquadratic Lyapunov function for continuous TS fuzzy models through their discretization

Since the beginning of the fuzzy control theory, results have been obtained independently for continuous and discrete models. It is still quite difficult to use nonquadratic Lyapunov functions for the continuous case, while this is much easier for the discrete case. This approach tries to put a bridge between the continuous and discrete cases for the class of continuous Takagi Sugeno fuzzy models that can be exactly discretized. Indeed, for this particular class, once the stability of the discrete model is ensured, the same control law applied to the continuous model will ensure the stability too. The interest of such an approach is that complex control laws and complex Lyapunov functions can be easily used. Simulation examples show that stabilizing feedbacks may be obtained with discrete control laws when purely continuous ones fail.