电子学报 ›› 2013, Vol. 41 ›› Issue (8): 1640-1646.DOI: 10.3969/j.issn.0372-2112.2013.08.030

• 科研通信 • 上一篇    下一篇

基于Picard迭代原理的非线性离散系统多频输入稳态响应的计算与分析

李博江, 胡钋, 文习山, 康基伟, 李洪江, 王战胜   

  1. 武汉大学电气工程学院, 湖北武汉 430072
  • 收稿日期:2012-05-25 修回日期:2013-05-15 出版日期:2013-08-25
    • 作者简介:
    • 李博江 男,1988年出生于江西南昌,武汉大学电气工程学院博士研究生,研究方向为电力系统过电压、电力系统稳定与控制、非线性系统控制理论与技术. E-mail:565052374@qq.com 胡 钋 男,1956年出生于湖北,博士,武汉大学电气工程学院教授,博士生导师,主要研究方向为非线性系统控制理论与技术、数字信号处理等.
    • 基金资助:
    • 中央高校基金科研业务费专项资金 (No.2012207020206)

A Solution and Analysis of Steady-State Responses of the Nonlinear Discrete Systems to Multiple Input Frequencies Based on Picard Iteration Principle

LI Bo-jiang, HU Po, WEN Xi-shan, KANG Ji-wei, LI Hong-jiang, WANG Zhan-sheng   

  1. School of Electrical Engineering, Wuhan University, Wuhan, Hubei 430072, China
  • Received:2012-05-25 Revised:2013-05-15 Online:2013-08-25 Published:2013-08-25
    • Supported by:
    • Fundamental Research Funds for the Central Universities (No.2012207020206)

摘要: 本文应用picard迭代原理和矩阵论中范数的理论提出了一种计算非线性离散系统多频输入稳态响应的方法,并给出了非线性离散系统多频输入稳态响应的通解.这种方法将一个非线性离散系统多频输入稳态响应计算问题化成计算同一个线性离散系统在不同输入下稳态响应的问题.文章用数学推导证明给出了多频输入的非线性离散系统存在唯一稳态响应的李普希次条件,并给出了判断一个非线性离散系统是否满足规定的李普希次条件的判定方法.基于所构建的求解方法,运用MATLAB语言编制了算法程序,对典型实例进行了仿真计算.大量仿真结果表明,本文提出的方法是正确的,且收敛速度较快.

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

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