B. Kosko, GLOBAL STABILITY OF GENERALIZED ADDITIVE FUZZY-SYSTEMS, IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART C-APPLICATIONS AND REVIEWS, 28(3), 1998, pp. 441-452
This paper explores the stability of a class of feedback fuzzy systems
. The class consists of generalized additive fuzzy systems that comput
e a system output as a convex sum of linear operators. Continuous vers
ions of these systems are globally asymptotically stable if all rule m
atrices 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 th
e discrete versions in the special but practical case of diagonal rule
matrices. The paper first reviews additive fuzzy systems and then ext
ends them to the class of generalized additive fuzzy systems, The Appe
ndix derives the basic ratio structure of additive fuzzy systems and s
hows how supervised learning can tune their parameters.