Relaxed Fuzzy Observer Design of Discrete-Time Nonlinear Systems via Two Effective Technical Measures

This paper deals with more relaxed designs of discrete-time Takagi-Sugeno fuzzy-model-based observers via two effective technical measures. Different from previous methods of this field, two effective technical measures are developed for obtaining more relaxed results, i.e., 1) A novel ranking-based switching mechanism is proposed by introducing a set of weighted variables so as to make use of the size differences information among normalized fuzzy weighting functions more freely. 2) A new slack variable method is proposed via the introduction of some extended representations for homogenous polynomials, and those major and minor relationships among all normalized fuzzy weighting functions are mapped to sole augmented multiindexed matrix for each homogeneous polynomial. Therefore, two positive results are provided in this paper, i.e., less conservative fuzzy observers can be given as a result of the above effective measures whilst a part of the online computational cost can be transferred to the offline implementation. Finally, two numerical examples are applied to illustrate the effectiveness of our approach.