非线性离散系统的Volterra泛函分析

Nonlinear Discrete Systems Via Volterra Series

本文根据Volterra泛函级数理论,提出了分析非线性离散系统振荡解的新方法,给出并证明了相应的幅频决定方程。与传统的方法和新近发展的方法相比,它不但具有这些方法的优点,而且不需要小参数的假设和可确定振幅是否足够小。同时,它是一种完全解析的符号化的频域方法,适于高阶离散动力系统与灵敏度分析。

A novel approach of determining the existences and the amplitude-frequency of oscillations in nonlinear discrete systems by solving a set of algebraic nonlinear equations. These determining equations can be generated to within any desired accuracy using a recursive algorithm based on severe restriction on either the degree of nonlinearily, or the amplitude of oscillation, and it is a frequency-domain symbolic approach applicable to any nonlinear discrete system with dynamics of any order, and sensitivity analysis.