Decay rate performance approach for stabilization continuous fuzzy models using their discretized forms

The purpose of this paper is to deal with the stabilization of the continuous Takagi Sugeno (TS) fuzzy models using their discretized forms based on the decay rate performance approach.

This approach is structured as follows: first, a discrete model is obtained from the discretization of the continuous TS fuzzy model. The discretized model is obtained from the Euler approximation method which is used for several orders. Second, based on the decay rate stabilization conditions, the gains of a non-PDC control law ensuring the stabilization of the discrete model are determined. Third by keeping the values of the gains, the authors determine the values of the performance criterion and the authors check by simulation the stability of the continuous TS fuzzy models through the zero order hold.

The proposed idea lead to compare the performance continuous stability results with the literature. The comparison is, also, taken between the quadratic and non-quadratic cases.

Therefore, the originality of this paper consists in the improvement of the continuous fuzzy models by using their discretized models. In this case, the effect of the discretization step on the performances of the continuous TS fuzzy models is studied. The usefulness of this approach is shown through two examples.