Applications of linear differential inclusion-based criterion to a nonlinear chaotic system: a critical review

In this study we present a neural network (NN)-based approach to represent a nonlinear Takagi-Sugeno system. A linear differential inclusion (LDI) state-space representation is utilized to deal with the NN models. Taking advantage of the LDI representation, the stability conditions and controller design are derived for a class of nonlinear systems. The controller design is based on the fuzzy control and parallel distributed compensation scheme, which is utilized to construct a global fuzzy logic controller by blending all local state-feedback controllers. Furthermore, this control problem can be reduced to linear matrix inequality problems by the Schur Complements. Efficient interior-point algorithms are now available in the Matlab toolbox to solve this problem. A chaotic system is simulated to show the feasibility of the proposed fuzzy controller design approach.