In this thesis, after the general introduction of the Takagi-Sugeno fuzzy model, we study the polynomial fuzzy model. The membership functions and state matrices of each subsystem of the Takagi-Sugeno model are obtained using a sector-nonlinearity method. The stability theorems are based on linear matrix inequality problems. The controller is constructed in this model with distributed parallel compensator. A polynomial fuzzy model of the theory is the generalization of the Takagi-Sugeno model, which in its later part are polynomial functions matrices. Also, its stability conditions are based on the sum of squares equations, and the controller in this model is obtained similarly to the Takagi-Sugeno model of distributed equilibrium. A polynomial fuzzy model using the sum of squares method has better stability conditions than the Takagi-Sugeno model and also works better with polynomials in dealing with complex systems and provides a simpler result. Since the sum of squares method, like the linear inequality of matrices, is a convex optimization problem, it is impossible to work with anomalous conditions, for example, bilinear conditions, in this thesis, the methods that have so far been used to solve this problem. Introducing the problem, also introducing a theorem and an algorithm to reduce the disturbance effect on the system output. The distinction between the algorithms introduced in this thesis and other similar tasks is to eliminate all the conservatism, as well as to provide a path to address the need for an explicit mathematical relation. Key Words: Polynomial fuzzy, T-S fuzzy, PDC, SOS approach, Stability, Robust stability, Min-Max optimization, Disturbance rejection, Sector nonlinearity.