Stability Analysis of Fuzzy Identification for Nonlinear Discrete Systems - Part I: Theoretical Study

This paper presents the stability analysis of parameter identification. The Takagi Sugeno fuzzy model is employed to represent the discrete time nonlinear dynamical systems. Once the structure of the fuzzy model is fixed, the parameters can be optimized. The parameter identification is accomplished by applying the gradient method where the iteration rates are specific to each parameter. The stability of this algorithm is discussed by using two approaches which guarantee that the system is stable if the iteration rates satisfy sufficient conditions. The first approach deals with the consequence parameters and the second one deals with the premise parameters.