New approach for the global analysis of fuzzy dynamical systems

Abstract

A novel approach for analyzing the global behavior of a fuzzy dynamical system is presented. It applies the concept and method of the cell-to-cell mapping to obtain the evolving trend of the states of the fuzzy dynamical system. The behavior of system is characterized by equilibria, periodic motions, and their domain of attractions. The min-max operation accumulates the fuzziness of a fuzzy system in every iteration and makes state evolution obscure. The proposed method transforms a given fuzzy mapping to a Z-to-Z mapping and does not accumulate fuzziness. Both the real and fuzzy initial state response analyses are discussed. An inverted pendulum controlled by a fuzzy controller is analyzed by the method to illustrate its validity.