In this note, we present some complementary results on the infinite horizon optimal control for linear time-delay systems. We formally establish some properties of the matrices arising in the Bellman functional, and we prove that any admissible linear control law generates only a class of Bellman functional for addressed systems. Additionally, experimental results are presented, which illustrate a satisfactory control performance when is compared with an optimal proportional integral industrial control.

中文翻译：

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线性时滞系统的贝尔曼泛函评述

在这篇笔记中，我们提出了一些关于线性时滞系统的无限视界最优控制的补充结果。我们正式建立了在贝尔曼泛函中出现的矩阵的一些性质，并且我们证明了任何可接受的线性控制律都只为寻址系统生成一类贝尔曼泛函。此外，还给出了实验结果，表明与最佳比例积分工业控制相比，其控制性能令人满意。