基于约束区间运算的区间线性微分方程组零解的稳定性

Stability of Zero Solutions of Interval Linear Differential Equations Based on Constrained Interval Algorithm

基于约束区间运算,本文研究了区间线性微分方程组的基本解矩阵,利用约束区间矩阵特征值,给出了区间线性微分方程组零解渐近稳定、稳定、不稳定的充要条件。具体的例子表明,区间线性微分方程零解的稳定性,不仅随着约束区间表达式中参数的变化而变化,个别问题也随着方程组维数的变化而变化。

Based on the constrained interval algorithm, this paper studies the fundamental solution matrix of interval linear differential equations, and gives the necessary and sufficient conditions for the asymptotic stability, stability and instability of the zero solution of interval linear differential equations by using the eigenvalues of the constrained interval matrix. Specific examples show that the stability of the zero solution of interval linear differential equations changes not only with the change of the parameters in the constrained interval expression, but also with the change of the dimension of some equations.