SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 581-599, February 2024.
Abstract. We consider an interconnection of a one-dimensional ODE and an infinite dimensional abstract differential equation in view of the asymptotic stability. Sufficient stability conditions are obtained under the assumption that the whole system is positive with respect to the Minkowski cone. The decoupled ODE subsystem is not required to be stable. We illustrate our results by means of examples demonstrating the advantages of the developed approach over the existing results. As well we compare our results with the known small-gain theory.

中文翻译：

---

具有可能不稳定组件的抽象互连系统的稳定性

SIAM 控制与优化杂志，第 62 卷，第 1 期，第 581-599 页，2024 年 2 月。
摘要。考虑到渐近稳定性，我们考虑一维常微分方程和无限维抽象微分方程的互连。在整个系统相对于闵可夫斯基锥为正的假设下，获得了充分的稳定性条件。解耦的 ODE 子系统不需要稳定。我们通过示例来说明我们的结果，证明所开发的方法相对于现有结果的优势。我们还将我们的结果与已知的小增益理论进行比较。