On the Estimation of Parameters of Takagi–Sugeno Fuzzy Filters

This study derives a class of filtering algorithms for Takagi-Sugeno fuzzy models via solving a nonlinear parameters estimation problem. The considered estimation problem is related to the problem of minimizing the expected value of the exponential of filtering errors energy. Under some stochastic assumptions, the filtering criteria (which involve an expectation operator) are replaced by the deterministic quadratic optimization problems whose solutions provide a class of fuzzy filtering algorithms. From a viewpoint of errors in the estimation of linear parameters of the fuzzy filter, the derived filtering algorithms were analyzed with emphasis on stability, robustness, and steady-state error issues. The stability and robustness analyses have been made deterministically without making any assumption.