This paper focuses on stabilization of second-order oscillatory systems using both feedback control and intentionally introduced time delay. The argument principle is employed as a key technique to divide the parameter space of time delay and controller gain into several regions. Every admissible value in these regions moves the poles of the closed-loop system towards the left of the complex plane such that stability improvement is achieved. The concept of potent asymptotic stability is first introduced, referring to the property that all the poles of the closed-loop system are stable and lie on the left of open-loop system poles in the complex plane. Analytical characterizations on parameter pairs of time delay and controller gain that result in potent asymptotic stability are established. All the poles and corresponding root locus with respect to gain are examined. Numerical examples and simulations are given to illustrate the usefulness and merits of the theoretical results.

本文着重于利用反馈控制和有意引入的时延来稳定二阶振荡系统。变元原理是将时间延迟和控制器增益的参数空间划分为几个区域的关键技术。这些区域中的每个允许值都会使闭环系统的极点移向复杂平面的左侧，从而实现稳定性的提高。首先介绍有效渐近稳定性的概念，指的是闭环系统的所有极点都是稳定的，并且位于复平面上的开环系统极点的左侧。建立了对时间延迟和控制器增益的参数对的分析表征，这些参数对导致有效的渐近稳定性。检查所有极点和相对于增益的相应根轨迹。数值算例和仿真结果说明了理论结果的实用性和价值。