线性时变系统的时域分析

Time-Domain Analysis of Linear Time-Varying Systems

提出了一类可解的高阶线性时变系统的时域分析方法。首先基于分离变量的基本思路,导出了一阶线性时变系统全响应的通解公式,然后将一类可解的二阶线性时变系统的非齐次微分方程转化成为两个关联的一阶线性时变系统的非齐次微分方程,借助一阶线性时变系统全响应的通解公式,导出了一类可解的二阶线性时变系统全响应的通解公式,有效解决了一类可解的高阶线性时变系统全响应的时域求解问题。

A time-domain analysis method for a class of solvable high-order linear time-varying systems is proposed. Firstly, based on the idea of separating variables, the general solution formula of full response for the first-order linear time-varying system is derived. Then, the non-homogeneous differential equations of a class of solvable second-order linear time-varying systems are transformed into non-homogeneous differential equations of two associated first-order linear time-varying systems. By using the general solution formula of full-response for the first-order linear time-varying system, a general solution of full response for a class of solvable second-order linear time-varying systems is derived, thus effectively solving the time- domain problem of a class of solvable high-order linear time-varying systems with full response.