This paper researches the static output‐feedback stabilization of single‐input single‐output (SISO) positive coupled differential‐difference equations (CDDEs) with unbounded time‐varying delays. First, a necessary and sufficient condition is provided for the positivity and asymptotical stability of CDDEs with unbounded time‐varying delays. For this type of system, based on the constructed estimates of its solution, a necessary and sufficient condition on asymptotical stability is provided. Then, based on this criterion, for CDDEs with unbounded time‐varying delays, a kind of static output‐feedback controller is designed to ensure the positivity and asymptotical stability of the corresponding closed‐loop systems. It is also worth pointing out that the controller is designed by the linear programming method without parameterization technique. This design approach can also be applied to the static state feedback stabilization problem of CDDEs with unbounded time‐varying delays. Finally, two illustrative examples are given to show the effectiveness of our results.

中文翻译：

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具有无界时变时滞的正耦合微分方程的稳定

本文研究了具有无限时变时滞的单输入单输出（SISO）正耦合微分方程（CDDE）的静态输出反馈稳定。首先，为CDDEs具有无限时变延迟的阳性和渐近稳定性提供了必要的充分条件。对于这种类型的系统，基于其解的构造估计，提供了渐近稳定性的必要和充分条件。然后，基于此标准，对于具有无限时变延迟的CDDE，设计了一种静态输出反馈控制器，以确保相应闭环系统的正性和渐近稳定性。还需要指出的是，控制器是通过不带参数化技术的线性编程方法设计的。这种设计方法还可以应用于具有无限时变延迟的CDDE的静态反馈稳定化问题。最后，给出两个说明性的例子来说明我们的结果的有效性。