关键词: 非线性离散系统, 多频输入, picard迭代, 李普希次条件, 数学推导

Abstract: In this paper,A method of computing steady-state responses of the nonlinear discrete systems to multiple input frequencies is presented by applying Picard Iteration Principle and knowledge of matrix theory and the general solutions of the nonlinear discrete systems to multiple input frequencies is given.By way of this algorithm,the steady-state responses of a nonlinear discrete system to the multiple input frequencies can be obtained by solving steady-state responses of the same linear discrete systems to different multiple input.In this paper,Lipschitz which can guarantee that there is a sole steady-state response of a nonlinear discrete system is presented through rigorous mathematical derivation and proof.The judging method is also presented to judge whether a nonlinear discrete system meet Lipschitz or not.Programs are developed using the MATLAB language based on the presented solution and plenty of typical examples are simulated to compute responses using these programs.Numerous computing results indicate that the method presented in the paper is correct and convergence is fast.

Key words: nonlinear discrete systems, multiple input frequencies, picard iteration, Lipschitz, mathematical derivation