Technical comments on the optimal control for linear distributed time-delay

Comments on the Bellman functional for linear time-delay systems

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 no concentrated delay term is present in the optimal control law.

Comments on the "Optimal strategy of deteriorating items with capacity constraints under two-levels of trade credit policy"

This technical note rectified the mathematical and conceptual errors present in Liao et al. (2014). Liao et al. (2014) proposed an EOQ model under two-levels trade credit policy considering limited storage capacity whereby the supplier provides a permissible delay period (M) to the retailer, and the retailer also offers a permissible delay period (N) (whereM > N) to its customers. In the current technical note, we point out some defects of their model from the logical viewpoints of mathematics regarding both interest charged and interest earned. Furthermore, as an example, one of the affected …

对V. L. Kharitonov《一类时滞系统的Lyapunov矩阵》的评论

Comments on: "Lyapunov matrices for a class of time delay systems" by V. L. Kharitonov

评论指出Kharitonov提出的二点边值问题边界条件线性相关，导致唯一解不存在，从而质疑其作为构造时滞系统Lyapunov矩阵基础的有效性。

对《基于Halanay型不等式的线性时滞系统事件触发镇定》的评论

Comment on "Event-Triggered Stabilization of Linear Time-Delay Systems via Halanay-Type Inequality"

本评论针对文献[1]中事件触发镇定分析的核心引理1，指出其证明存在技术漏洞并给出修正论证，确认原始引理表述仍成立。

A Study on Accelerating Average Consensus Algorithms Using Delayed Feedback

In this paper, we study accelerating a Laplacian-based dynamic average consensus algorithm by splitting the conventional delay-free disagreement feedback into weighted summation of a current and an outdated term. We determine for what weighted sum there exists a range of time delay that results in the higher rate of convergence for the algorithm. For such weights, using the Lambert W function, we obtain the rate increasing range of the time delay, the maximum reachable rate and comment on the value of the corresponding maximizer delay. We also study the effect of use of outdated feedback on th…