Noise elimination of nonlinear systems using Takagi-Sugeno model

In the old paper of Mukhopadhyay and Narendra, the problem of disturbance rejection in the control of nonlinear systems with additive disturbance generated by some unforced dynamical systems, was formulated and solved by using neural networks for several models of varying complexity, but the purpose of this paper is how using the fuzzy set systems in the problem of disturbance rejection, and to provide theoretical justification to existence of solution. The objective is to determine the identification model and the control law to minimize the effect of the disturbance at the output. In all cases, several stages of increasing complexity of the problem are discussed in detail. Two simulation studies based on the results discussed are included towards the end of the paper.