State-feedback H∞ switching control for Takagi-Sugeno fuzzy systems based on partitioning the range of fuzzy weights

In this study, an H_∞ state-feedback controller for continuous-time Takagi-Sugeno (T-S) fuzzy systems, where the membership functions are assumed to be non-differentiable, is considered. The salient feature over the existing results is that this study gives an idea of applying the well-known matrix elimination lemma as a means to reduce the order of the fuzzy weights from the given condition: by augmenting the fuzzy weights in conformity with the matrix elimination lemma, the order of the fuzzy weights in the original quadratic condition is decreased and a decision variable that is dependent on the fuzzy weights is introduced in a more tractable form. Then, this time-varying decision variable is approximated piecewisely by partitioning the range of the fuzzy weights, and the negativity of the corresponding relaxed condition is checked by utilising the extreme points for each partition so that a switching control scheme based on the partition can be obtained. Some simple examples are given to demonstrate the effectiveness of the proposed criterion.