A new approach to relaxed stability conditions of fuzzy control systems

In this paper a new approach for the stability analysis of Takagi-Sugeno (T-S) fuzzy systems is proposed. Because of low numbers of linear matrix inequality (LMIs) or bilinear matrix inequality (BMIs) and independence of this method of finding only one symmetric positive definite matrix makes this method highly applicable and has less computation. Such that for a conventional method which is used for stability analysis, computation length is decreased drastically. Also, the conditions on the shape of fuzzy sets have high latitude which make this method more useful. Based on the properties analysis of the Takagi-Sugeno (T-S) fuzzy systems with two-overlapped fuzzy sets, at first we introduce a method that decreases LMIs (BMIs) and computations. Then based on this approach a typical theorem will be introduced. To demonstrate the new approach, we apply it to a mass-spring-damper system.