Fuzzy feedback system analysis using transition matrices

An analytical characterization of fuzzy feedback systems based on transition matrices is carried out in this paper. The analysis faces both systems which use linear operators (sum and product) and those based on the max–min operators. We focus on the asymptotic trend of the system when the external input is held constant; such study becomes a matrix convergence problem by means of the transition matrices that define the system behavior. For the non-linear case a sufficient condition of convergence of the system (that, in particular, avoids oscillations) is demonstrated.