A new linear matrix inequation (LMI) approach is studied for a class of continuous Nonlinear System, which is simple and easy to use. By means of interpolation analysis, the precondition that the closed -loop Nonlinear System is asymptotically stable is reduced to that each of a group of linear matrix inequations is separately solvable. Firstly, employing Neville's algorithm and Newton's Interpolation formula that are used to construct Lagrange interpolation polynomial, we deduce that a class of Nonlinear matrix inequation on D is solvable if and only if each of a group of linear matrix inequations is solvable. Furthermore, the expression of relation between the solution of Nonlinear matrix inequation and the solutions of linear matrix inequations is obtained. Then using the above Nonlinear matrix inequation, we can get the nonlinear state feedback solution such that the closed-loop Nonlinear System is asymptotically stable. Under the feedback control, the region of attraction can be estimated. Finally, the effectiveness and the correctness of this method is validated by a numerical simulation.
