线性模型中二阶微分方程的超稳定振动性定理

Super Stable Oscillation Theorems for Two Order Differential Equations in Linear Model

分析线性模型中二阶微分方程的超稳定振动性,为解决系统的稳定性控制问题提供数学理论基础。对线性模型中二阶微分方程的超稳定性进行幅相裕度优化控制研究,构建二阶微分方程,采用向量Lyapunov函数方法进行了时滞相关特征分解,在异变平衡点分解中采用幅相裕度优化控制方法对微分系统的时滞参数进行稳定性分析,得到了线性模型中二阶微分方程超稳定解,给出了超稳定振动性定理,数学分析得出,线性模型中的二阶微分方程具有超稳定振动性特征,给出的超稳定振动性定理可靠,微分方程的特征解是稳定收敛的,以此指导稳定性控制,提高控制精度和可靠性。

The ultra stable oscillation of the two order differential equations in the linear model is analyzed, and it provides the basis for solving the stability control problem of the system. Super stability of two order differential equations in the lin-ear model of amplitude control of optimization of the phase margin, constructing two order differential equations, using the vector Lyapunov function method decomposes the delay dependent feature, the amplitude and phase margin optimization control method to analyze the stability of time delay differential system decomposition in the alteration of the balance point, get the linear model of two order differential equations of super stable solution, given the ultra stable oscillation theorem, mathematical analysis, two order differential equations in the linear model has the characteristics of ultra stable oscillation, super stable oscillation theorem gives reliable features, the solution of differential equation is stable and convergent, so as to guide the stability control, improve the accuracy and reliability of the control.