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Some issues on coordinate transformations of T‐S fuzzy models

As a mathematical model to represent the dynamics of a plant to be controlled, the T‐S fuzzy model is widely used in the control system design. In order to facilitate controller design, it sometimes needs suitable coordinate transformations of the T‐S fuzzy model. Subsequently, some questions arise: (1) can local systems in different fuzzy rules perform different coordinate transformations? if yes, then (2) is the transformed T‐S fuzzy model equivalent to its original one? In answering these questions, this paper at first gives a brief review on the T‐S fuzzy model to catch the real meaning of local systems in the context of the whole system expressed by the T‐S fuzzy model. Then, bearing controller design in mind it discusses the equivalence between pre‐ and transformed systems in various types of T‐S fuzzy models. Finally, in order to share the benefits from the results discussed in this paper, a controller design based on an affine T‐S fuzzy model is provided. © 2020 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.