This paper presents a new method to find $\alpha$-exponential state estimates, where $\alpha >0$ is a given decay rate, for a class of positive systems with bounded time-varying delays. Here, our novel idea is to construct a new class of “comparison” systems, from which we can derive a smaller factor vector for an $\alpha$-exponential estimate on the solution of the considered system, i.e. derive a tighter $\alpha$-exponential state estimate. The effectiveness of the presented method is illustrated through a numerical example.

中文翻译：

---

对具有时间延迟的正系统进行更严格的指数估计

本文提出了一种新的查找方法$\alpha$-指数状态估计，其中$\alpha >0$是给定的衰减率，对于具有有界时变延迟的一类正系统。在这里，我们的新想法是构建一类新的“比较”系统，我们可以从中得出一个较小的因子向量$\alpha$- 对所考虑系统的解的指数估计，即推导出更严格的$\alpha$-指数状态估计。通过数值例子说明了所提出方法的有效性。