It is shown that a positive linear system on a time scale with a bounded graininess is uniformly exponentially stable if and only if the characteristic polynomial of the matrix defining the system has all its coefficients positive. Then this fact is used to find necessary and sufficient conditions of positive stabilizability of a positive control system on a time scale.

中文翻译：

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时间尺度上线性正系统的稳定性和稳定性

结果表明，当且仅当定义系统的矩阵的特征多项式的所有系数都为正时，带有有限粒度的时间尺度上的正线性系统才是指数稳定的。然后，使用该事实在时间范围内找到阳性控制系统的阳性稳定性的必要条件和充分条件。