This paper is concerned with the problems of finite-time boundedness and finite-time control for positive coupled differential-difference equations (CDDEs) with bounded time-varying delay. The finite-time stability of such systems is analyzed by constructing an estimate of the solutions over a finite time interval. And, sufficient conditions based on linear programming (LP) are provided for finite-time stability of positive CDDEs with bounded time-varying delay. Then, by coordinate transformation, the obtained results are extended to the finite-time bounedness of positive CDDEs with bounded time-varying delay. By the obtained result of finite-time boundedness, static output-feedback controllers and static state-feedback controllers are designed and a sufficient condition is derived to ensure the positivity and finite-time boundedness of closed-loop system. Three illustrative examples are given to show the validity of our results.

本文关注时变时滞有界的正耦合微分方程(CDDE)的有限时间有界性和有限时间控制问题。这种系统的有限时间稳定性是通过在有限时间间隔内构建解的估计来分析的。并且，基于线性规划 (LP) 的充分条件提供了具有有界时变延迟的正 CDDE 的有限时间稳定性。然后，通过坐标变换，将得到的结果推广到具有有界时变延迟的正 CDDE 的有限时间有界。由有限时间有界得到的结果，设计了静态输出反馈控制器和静态状态反馈控制器，并推导出一个充分条件来保证闭环系统的正性和有限时间有界性。给出了三个说明性的例子来表明我们结果的有效性。