Abstract

In order to get the best corresponding answer in accordance with a reference model signal, digital filters should have the minimum error at its output using the mean square criterion. Inserting a fuzzy mechanism into its internal structure to construct an intelligent filter, the reference signal was adaptively interpreted to select and emit a decision answer in accordance with external reference signal changes, thereby updating the best correct new conditions into a process dynamically. The fuzzy filter gets the interpretation of the input signal level selecting the best weight parameter values from a set of membership functions stored into the knowledge base (KB), in order to give a signal approximation of the reference signal in natural form. The fuzzy stage improves the filter answers minimizing its convergence error using a classification of its operation into levels considering the minimum error distance. This work describes the stability properties of the fuzzy filter in accordance with the Kharitonov’s polynomials theory that establishes the maximum and minimum limits intervals of the fuzzy filter and the Routh-Hurwitz criterion to get the stability analysis of the filtering process. The states of the fuzzy filtering require that all of its answers bound into the error criteria probabilistically, in accordance with the Nyquist and Shannon assumptions and finally the paper shows the simulations of the fuzzy filter into the Kalman structure using the Matlab^© tools.

Key words: Digital filtering, fuzzy systems, estimation, stability.