A description of the dynamic behavior of fuzzy systems

An approach is presented for analyzing the global behavior of a fuzzy dynamical system that applies the concept and method of cell-to-cell mapping to obtain the evolving trend of the states of a fuzzy dynamical system. The behavior of the fuzzy system is characterized by equilibria, periodic motions, and their domain of attractions. Min-max operation accumulates the fuzziness of a fuzzy system in every step of iterations and makes the state evolution obscure. The proposed method transforms a given fuzzy mapping to at 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 to illustrate the validity of the method