Stability analysis of fuzzy controll systems simplified as a discrete system

Fuzzy controls can describe control rules using fuzzy if-then rules and it can incorporate experts' control rules. It is, however, difficult to guarantee the stability of fuzzy control system. This paper presents a new method for stability analysis of fuzzy control system using petri nets. The proposed method crisply divides all of the input and output variables of the fuzzy controller and the fuzzy model of the controlled object. This crisp division makes the fired rules of the fuzzy controller and the fuzzy model, which have truth values greater then 0, be single each. These simplified fuzzy rules can be considered as discrete description of the controller and the controlled object. By approximating and the fuzzy control system as this discrete system, the system can be expressed by the petri nets. The proposed method describes the fuzzy control system using matrix based on a bipartite directed multigraph of the petri net, thereby enables to analyse the stability of the fuzzy control system. The analytic results using the petri nets have clear correspondence to the fired fuzzy rules. The dynamical behavior of the system are able to be understood easily. Simulation is done to verify the proposed stability analysis method.