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This paper proposes direct adaptive fuzzy control with less restriction on control gain for siso nonlinear systems and is presented a simplified type-2 fuzzy system. Adaptation law is derived based on Lyapunuv stability analysis that assures adaptive parameters and tracking error to be bonded. Since in addition to consequent parameters,width and centers of the membership functions are tuned then the estimation error is very small so as to be negligible.Furthermore, the number of membership functions required is seen to be less than that needed with type-1 fuzzy sets. The simulation results that are conducted on inverted pendulum and magnetic levitation systems confirm the efficacy of the proposed scheme. In the presence of noise the reference input is tracked very well and tracking error is very small.

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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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This paper is concerned with the problem of improvement of fuzzy H_infinity tracking controller for nonlinear systems modeled by T-S fuzzy scheme. The fuzzy tracking controller not only stabilizes the closed-loop system, but also results in the H_infinity tracking error norm to all the bounded external signals to be less than some given value. A new tracking control law is proposed for each linear local subsystem of T-S fuzzy model. A Linear Matrix Inequalities (LMIs) approach is proposed to find all the parameters of the control laws. The proposed approach results in a noticeable improved tracking performance with respect to the existing approaches. An investigation of the tracking performance of the proposed approach on the inverted pendulum system, in comparison with the other approaches, shows the improvement.