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In this paper, we investigate the design method for interval type-2 (IT2) T-S fuzzy controller based on IT2 T-S fuzzy observer for nonlinear systems along with uncertainty parameters. In order to analyze the stability and synthesis the control methods conveniently, an IT2 (T–S) fuzzy model is applied through representing the dynamic of nonlinear systems and dynamic of observer. Uncertainty parameters are captured by IT2 membership function characterized by the lower and upper membership functions. In this paper, for IT2 fuzzy controller, the membership functions and number of rules can be freely chosen different from the IT2 T–S fuzzy model and IT2 T-S fuzzy observer. This method is known non- Parallel Distributed Compensation. To reduce the conservativeness of stability analysis, a fuzzy Lyapunov function candidate is applied. The stability conditions in term of linear matrix inequlities (LMIs) are obtained.

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In this study a model reference rough-radial basis function neural network controller with feedback error learning for control of a class of nonlinear systems subject to unknown bounded uncertainty is proposed. The proposed controller in hybrid form includes the classic controller and rough- radial basis function neural network controller. Because of using the classic controller with the neural network controller, it is expected that the transient response is bounded. The weights of the output layer of the neural network controller are interval variables. Using an appropriate Lyapunov function, stable adaptation laws for these weights according to the output of the classic controller and based on stability are derived. To show the efficacy of the proposed controller, results of simulation that is applied to Duffing Oscillator and Genesio- Tesi are shown and results are compared with the results when simple model reference radial basis function neural network is used as the controller. The results show that the proposed method is more robust against uncertainty when it is compared to model reference radial basis function neural network controller. Also, using the proposed controller, synchronization of chaotic systems is performed. The results verified the effectiveness of the proposed controller.