A Theory on Stability of Fuzzy Control System Using Discrete Event Representation and Numerical Analysis on Transition between Events

Abstract

Fuzzy control rules are described with if-then expressions, and the fuzzy controls can incrorporate experts' control rules. It is, however, difficult to guarantee the stability of fuzzy control system. Studies have been done to analyze the stability of fuzzy control system. These studies are effective to analyze the stability of the fuzzy control system. However, the distinguishing feature of fuzzy controls, i.e.easily understandable linguistic expressions, have not been utilized in these analyses. A new method for stability analysis of fuzzy control systems using petri nets has been proposed. By simplifying the fuzzy control system as a discrete system, the fuzzy control system can be expressed using the petri nets. The transitions in the petri nets have one-to-one correspondence with fuzzy rules, and it is easy for us to comprehend the behavior of fuzzy control systems from the petri nets. The difficulty of this method is that the stability of the control system is guaranteed by manually following the firing sequences in the petri nets. This paper presents a new representation of fuzzy control system using matrix based on a bipartite directed multi-graph, and derives a theory of asymptotic stability. This approximation sacrifices the rigorous description of the behavior of the fuzzy control system. This paper also studies a method to analyse transitions between fuzzy sub-regions using numerical expressions. Simulation is done to verify the proposed stability analysis method.