Synthesis of fuzzy controllers that achieve linguistic performance objectives

We use a new theorem about obtaining the fuzzy relation of a closed-loop feedback system given the fuzzy relations of the plant and the controller. Based on this theorem, a new design procedure of a fuzzy controller is proposed. To understand concepts, an example is used throughout the paper. Then, based on the fuzzy rules giving the desired behavior of the closed-loop system and given the fuzzy relation describing a plant, the design procedure is applied to synthesize a fuzzy controller.