Feedback linearization for input-saturation nonlinear system based on T-S fuzzy model

Considering input saturation problem of nonlinear system, a linearized model of multi-inputs nonlinear system is proposed in this paper. The final linear model has prescribed poles and has the same convergence nearby the designed equilibrium points. After this, the linear control theorem can be applied. During the calculation of linearization, T-S (Takagi Sugeno) fuzzy model and pole placement method were utilized. Pole placement just was applied only once for the final model comparing the traditional case where it was designed for every fuzzy rule. This means fewer LMIs (linear matrix inequality) will be needed and its solution will be guaranteed as much as possible. In this paper, nonlinear system will be transferred to T-S fuzzy model first. Note that the T-S fuzzy model is still nonlinear. Then, by employing a series of transfer matrix, nonlinear T-S fuzzy model will be transferred into a nearly linear form accompanied with only one nonlinear part. Finally, by designing a proper controller, linear pole placement method is used and the designed linearization controller gains can be calculated out with LMIs.