Ellipsoidal approximation of reachability sets of a class of nonlinear systems represented by the Takagi-Sugeno fuzzy models

Abstract

An approach that allows approximating reachability sets of a class of nonlinear systems under bounded exogenous disturbances is presented. Its implementation includes two stages. At the first stage the transition to fuzzy description is performed. A nonlinear system is replaced by the equivalent Takagi-Sugeno fuzzy model. This allows describing the behavior of the initial system in the given area of the phase space via a set of linear models weighted by membership functions. At the second stage the reachability sets of the system are estimated on the basis of generalization of the method of invariant ellipsoids. The numerical testing results that allow assessing the conservatism of the obtained estimations are presented.