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In this paper, an analytical approach to characterize discrete Tanaka Sugeno Kang (TSK) fuzzy systems is presented. This characterization concerns the choice of the adequate conjunctive operator between input variables of discrete TSK fuzzy models, t-norm, and its impact on stability domain estimation. This new approach is based on stability conditions issued from vector norms corresponding to a vector-Lyapunov function. In particular, second order discrete TSK models are considered and this work concludes that Zadeh's t-norm, logic product min, gives the largest estimation of stability domain.

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Abstract-A new design method internal model control is proposed for multivariable over-actuated processes that are often encountered in complicated industrial processes.Due to the matrix that is adopted to describe over-actuated system is not square, many classical multivariable control methods can be hardly applied in such system. In this paper, based on method of virtual outputs, a new internal model control method is proposed.The proposed method is applied to shell standard control problem (3 inputs and 2 outputs). The simulation results show that the robust controller can keep the set inputs without overshoot, steady state error, input tracking performance and disturbance rejection performance, the results are satisfactory have proved the effectiveness and reliability of the proposed method. Keywords-internal model control (IMC); over-actuated multivariable system; inverse model; method of virtual outputs; disturbances rejections, stability; state error

Abstract-An internal multimodel control designed for nonlinear multivariable systems, is proposed in this paper. This approach is based on the multi-modeling of nonlinear systems and the realization of a specific inversion of each model. A comparative study is presented between two structures of the internal multimodel control. The first one is based on switching models and the second on residues techniques as fusion method. The case of a second order nonlinear multivariable system shows the effectiveness of both structures.

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