Abstract

Various tests for the exponential stability of a linear system of ordinary differential equations are obtained by the method of frozen coefficients. To this end, we prove and use an improved Gelfand–Shilov estimate for the matrix exponential. The cases in which the coefficient matrix of the system satisfies the Lipschitz condition or the Hölder condition on the positive real line are considered separately.

中文翻译：

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Hölder 条件下的冻结系数方法

摘要

常微分方程线性系统的指数稳定性的各种检验是通过冻结系数的方法获得的。为此，我们证明并使用改进的 Gelfand-Shilov 估计矩阵指数。系统的系数矩阵满足正实线上的Lipschitz条件或Hölder条件的情况分别考虑。