Global stability of generalized additive fuzzy systems

This paper explores the stability of a class of feedback fuzzy systems. The class consists of generalized additive fuzzy systems that compute a system output as a convex sum of linear operators. Continuous versions of these systems are globally asymptotically stable if all rule matrices are stable (negative definite). So local rule stability leads to global system stability. This relationship between local and global system stability does not hold for the better known discrete versions of feedback fuzzy systems. A corollary shows that it does hold for the discrete versions in the special but practical case of diagonal rule matrices. The paper first reviews additive fuzzy systems and then extends them to the class of generalized additive fuzzy systems. The Appendix derives the basic ratio structure of additive fuzzy systems and shows how supervised learning can tune their parameters.