Fuzzy Systems—Sets, Logic, and Control
Thrishantha Nanayakkara, Ferat Sahin, Mo M. Jamshidi · 2018
This chapter overviews classical and fuzzy sets, classical and fuzzy logic, and fuzzy control systems and their stability. It presents the issues that are important in understanding fuzzy sets and their advantages over classical sets. Fuzzy control systems are very desirable in situations where precise mathematical models are not available and human involvement is necessary. In such cases, fuzzy rules could be used to mimic human behavior and actions. Stability of fuzzy control systems was also discussed, including the Lyapunov stability. The chapter discusses some results of Tanaka and Sugeno with respect to analysis of feedback fuzzy control systems. It would use Takagi-Sugeno models to develop fuzzy block diagrams and fuzzy closed-loop models. The chapter presents an up-to-date survey of available techniques and tests for fuzzy control system stability. The stability test for fuzzy control systems, or lack of it, has been a subject of criticism by many control engineers in some control engineering literature.