On the stabilization of continuous fuzzy models using their discretized forms

This paper proposes a new method to stabilize the continuous-time TS fuzzy models by using results from their discretized models. The proposed approach is structured as follows: first, a discrete model is obtained from the discretization of the continuous TS fuzzy model. Second the gains of a non-PDC controller ensuring the stabilization of the discrete model are determined. Third, we check if the discrete control law used continuously without any zero-order hold can stabilize the continuous TS model. It is obvious that two sets of LMIS conditions are obtained: one for the discrete model, and one for the continuous on. But these two sets of LMIS conditions are much easier to solve than a single set of BMIS conditions usually found when a non PDC control law is directly applied to a continuous model. Simulation examples illustrate the effectiveness of this approach.