Abstract In this article, the problem of stabilization for the switched positive linear system (SPLS) with impulse and marginally stable subsystems is studied, in which both the continuous time case and the discrete time case are taken into account. By the usage of a piecewise weak linear copositive Lyapunov function (LCLF) and the mode-dependent dwell time (MDT), time-dependent switching control laws are designed to guarantee the asymptotic stability of the system. Furthermore, based on the comparison principal for positive systems, the main results are generalized to the time-variant SPLS. Two examples are worked out to indicate that our results have advantages over some known results in the literature.

中文翻译：

---

具有脉冲和边际稳定子系统的开关正系统的稳定性：一种依赖于模式的驻留时间方法

摘要 本文研究了具有脉冲和边际稳定子系统的切换正线性系统（SPLS）的镇定问题，其中考虑了连续时间情况和离散时间情况。通过使用分段弱线性共正李雅普诺夫函数 (LCLF) 和依赖于模式的驻留时间 (MDT)，设计了依赖于时间的切换控制律来保证系统的渐近稳定性。此外，基于正系统的比较原理，主要结果被推广到时变 SPLS。计算出两个例子来表明我们的结果比文献中的一些已知结果具有优势。