Stability in feedback additive fuzzy systems

Feedback fuzzy systems take their own output as input and define nonlinear rulebased dynamical systems. They use a fixed number of rules to model other dynamical systems while feedforward fuzzy systems suffer from exponential rule explosion. But most feedback fuzzy systems are not themselves stable. Generalized additive fuzzy systems are a special class of feedback fuzzy systems that compute a system output as a convex sum of linear operators. A matrix replaces each then-part fuzzy set function in a standard fuzzy system. The paper proves that continuous versions of these feedback systems are globally asymptotically stable if all rule matrices are stable (negative definite). This does not hold for the better-known discrete version of Tanaka. A corollary shows that it does hold for a special but practical case of the discrete additive model.