Fuzzy Remodeling and Synthesys of the Class of Nonlinear Systems Based on the Invariant Ellipsoid Technique

An approach that allows performing the synthesis of a class of nonlinear systems under bounded exogenous disturbances is presented. Its implementation includes two stages. At the first stage the given nonlinear system is replaced by the equivalent Takagi-Sugeno fuzzy model. At the second stage via generalization of the method of invariant ellipsoids we solve the problem of finding fuzzy control that stabilizes the closed-loop system and provides optimal rejection of the effect of exogenous disturbances. The numerical testing results showing the efficiency of the offered method are presented.