摘要
分段定常系统在微分方程稳定性理论及应用中,特别是在现代科学技术实践中,是一种常见的数学模型。如时变线性微分方程的冻结系统往往就是分段定常系统([1][2])。在文[3]中研究了三阶无界分段定常系统。本文将讨论n阶分段定常系统解的上、下指数并以上下指数为特征将其解空间分解为若干子空间的直接和。所得结论对其稳定性研究和定性研究都提供了重要依据。
In this paper, we discuss the exponent of n-order differential equations with unbounded piecewise-constant matrix, and resolve it's solution space into the direct sum of independent subspaces on the basis of it's exponent. Our results are provide important basis for stability and qualitative study.
