Stability properties of fuzzy controllers

One of the main objections to fuzzy control compared to classical control engineering is the lack of stability proofs. The paper will give an overview of the existing methods for evaluating and testing the stability of fuzzy controllers. Special attention will be paid to the identification of the implicit and explicit assumptions and restrictions necessary for the various methods of stability proofs. It will be shown that the methods used for proving stability are especially suitable for a particular class of fuzzy controller structures. The second part of the paper will focus on the design of fuzzy controllers with the stability aspect in mind. A careful selection of linguistic variables, membership functions, inference types etc. will result in the design of a more robust controller. The effects of these methods on the design of fuzzy controllers will be illustrated by a practical tank storage problem.