Fuzzy rules reduction for discrete-time T-S fuzzy systems based on regional piecewise approach

This paper combines the fuzzy region concept and the piecewise Lyapunov stability criterion to design a new fuzzy controller which is called piecewise Takagi-Sugeno (T-S) fuzzy region controller. The original controller design of T-S fuzzy region concept is required to find the common Lyapunov matrix. This common positive definite matrix may not exist when the T-S fuzzy system includes many fuzzy rules. Now we utilize the piecewise Lyapunov stability criterion and the regional concept to find the individual Lyapunov matrix for each region. Therefore, this proposed condition is less conservative. The piecewise Lyapunov stability criterion is expressed in terms of linear matrix inequalities (LMIs). Finally, a numerically example is given to illustrate the usefulness of the proposed approach.