Fuzzy Stabilization of Nonlinear Systems under Sampled-Data Feedback: An Exact Discrete-Time Model Approach

This paper addresses stabilization problems for a nonlinear system via a sampled-data fuzzy controller. The nonlinear system is assumed to be exactly modeled in Takagi-Sugeno´s form, at least locally. Unlike the conventional direct discrete-time design approach based on an approximate discrete-time model, the sampled-data fuzzy controllers are designed based on an exact discrete-time model. Sufficient design conditions are formulated in terms of linear matrix inequalities. It is shown that whenever the exact discrete-time fuzzy model is asymptotically stabilizable via the sampled-data fuzzy controller uniformly bounded in the state, then so is the original nonlinear system. A numerical example is given to illustrate the effectiveness of the proposed methodology.