We obtain efficient exponential stability tests for a system $\dot{x}\left(t\right)=A\left(t\right)x\left(h\left(t\right)\right),$ where $A$ is a block matrix and $h\left(t\right)$ is a delay function, in terms of norms and matrix measures of blocks. Compared to the analysis of the whole matrix $A$, handling blocks can be more manageable even for the system $\dot{x}\left(t\right)=A\left(t\right)x\left(t\right)$ without delay. In a presented example, the criterion applied to $A$ fails, while considering appropriate blocks leads to exponential stability. Another example illustrates efficiency even in the case of a non-delay system.

中文翻译：

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具有块矩阵的时滞微分方程组的指数稳定性。

我们获得了系统的有效指数稳定性测试 $\dot{X}（Ť）=\mathrm{一种}（Ť）X（H（Ť）），$ 在哪里 $\mathrm{一种}$ 是一个块矩阵， $H（Ť）$就块的范数和矩阵度量而言，是一个延迟函数。与整个矩阵的分析相比$\mathrm{一种}$，即使对于系统，处理块也可以更易于管理 $\dot{X}（Ť）=\mathrm{一种}（Ť）X（Ť）$不延误。在给出的示例中，该准则适用于$\mathrm{一种}$失败，而考虑适当的块会导致指数稳定性。另一个示例说明了即使在非延迟系统的情况下的效率。