This article aims to design proportional-derivative (PD) controllers for interval positive linear systems in the continuous-time domain, which still remains a widely-discussed open problem in positive systems theory. The specific objective is to design a PD controller for the system with interval uncertain parameters and time-varying delay, which simultaneously ensures closed-loop system stability and preserves positivity. The work proposes a systematic framework, with the aim of finding PD controller gains for positive robust stabilization. The methodology and algorithm are presented first in the study, and the performance of such methods is instantiated by numerical examples.

本文旨在为连续时间域中的区间正线性系统设计比例微分 (PD) 控制器，这仍然是正系统理论中一个广泛讨论的开放问题。具体目标是为具有区间不确定参数和时变延迟的系统设计PD控制器，同时保证闭环系统的稳定性和保持正性。这项工作提出了一个系统框架，目的是寻找 PD 控制器增益以实现积极的稳健稳定。研究中首先介绍了方法和算法，并通过数值例子说明了这些方法的性能。