标题： 一种用于带有时间延迟的1-D波动方程稳定性分析的新方法 显示英文标题

标题： A new approach for stability analysis of 1-D wave equation with time delay

摘要： 在我们的手稿中，我们开发了一种新的方法用于带有时间延迟的一维波动方程的稳定性分析。 我们工作的主要贡献是开发了一种新的谱分析方法。 我们推导了保证闭环系统指数稳定性的反馈增益和时间延迟的充分必要条件。 与过去文献中开发的类似条件相比，我们讨论了时间延迟为正的所有情况，包括当它为无理数时的情况。 我们证明，当且仅当时间延迟为偶数时，可以实现指数稳定性。 我们还得到了不同时间延迟偶数倍下的耦合增益稳定性区域的一般公式项，并由此很容易得出随着时间延迟增加稳定性区域缩小的情况。 此外，我们探讨了时间延迟的微小扰动对高频鲁棒性的影响。 显示英文摘要

摘要： In our manuscript, we develop a new approach for stability analysis of one-dimensional wave equation with time delay. The major contribution of our work is to develop a new method for spectral analysis. We derive sufficient and necessary conditions for the feedback gain and time delay which guarantee the exponential stability of the closed-loop system. Comparing with similar conditions developed in the past literatures, we discuss all the situation when the time delay is positive, including when it is irrational. We prove that the exponential stability can be achieved if and only if the time delay is an even number. We also get the general formula term of the stability region of the coupling gain for different even multiples of time delay, and from this we easily obtain the shrink of the stability region as time delay increases. In addition, we explore the impact of slight perturbations in time delay on high frequency robustness.