T-S fuzzy model with linear rule consequence and PDC controller: a universal framework for nonlinear control systems

We present two results concerning the fuzzy modeling and control of nonlinear systems. The first result is on the approximation of smooth nonlinear dynamical systems using linear Takagi-Sugeno (T-S) fuzzy models. The second result is on the approximation of smooth nonlinear state-feedback controllers using the so-called parallel distributed compensation (PDC) controller. Both results are based on the effectiveness of using linear Takagi-Sugeno systems to approximate nonlinear function, which is also proved in this paper