H∞ controller of Nonlinear System basing on the lagrange interpolation polynomial

This paper uses interpolation polynomial method to approximate Nonlinear System. The Interpolation polynomial adopted in this methodology is a combination of Lagrange´s interpolation polynomials, which are obtained by Aitken interpolation formula step by step. During the constructing of the interpolation polynomial, we infer a sufficient condition such that Nonlinear System has limited L₂-gain. The sufficient condition is a group of linear matrix inequations, which can be solved by LMI toolbox of Matlab. Moreover, a state feedback control law is presented.