Analytical structures of fuzzy constroller under different fuzzy membership degrees

Analytical structure of fuzzy controller has recovered two important issues: why fuzzy controller is useful in application and what relationships are there between fuzzy controller and the most used PID controller. But these existing outcomes are uniformly studied under the conditions that all fuzzy rules are taken the same fuzzy membership degrees. This is not real in some applications since some fuzzy rules have likely different certainties or fuzziness. In this paper we study the analytical structure of fuzzy controller in this case that some fuzzy rules take different membership degrees, in graphical comparison with the existing fuzzy control system. The deriving outcomes generalize the existing results and thus have widely applicable range. An example is used to demonstrate our viewpoints.