中文摘要：

讨论在平均驻留时间的切换下,连续线性切换正系统的稳定性问题。切换系统的稳定性是切换系统研究的重要内容。在很多实际的应用中,一个切换系统的稳定性的高低直接决定这个系统性能的好坏。如果系统的切换规则是任意的,那么系统的性能会更好。然而,对于一个线性切换正系统,要想使得系统稳定必须存在一个余正李雅普诺夫函数,且函数的微分沿着系统轨迹是负的。所以首先要给出余正李雅普诺夫函数的定义,再结合线性矩阵不等式等知识求出余正李雅普诺夫函数的微分。应用线性切换正系统的一些性质,得到线性切换正系统在平均驻留时间切换下系统稳定的充分必要条件。最后,一个数值例子验证问题的有效性。

英文摘要：

This paper considers the problem of stability for a class of continuous-time switched positive linear system with average dwell time switching. The stability of switched systems is an important part of the study of switched systems. In many applications, the stability of a switched system directly determines the performance of the system. If the switched rule is arbitrary, the system＇s performance will be better. In order to make the system stable, the differential of eopositive Lyapunov Function along the system trajectory is negative. Firstly, a linear copositive Lyapunov Function is introduced and get differential of copositive Lyapunov Function by linear matrix inequality. A stability criterion is proposed for the linear switched system under an average dwell time switching by the properties of linear positive system. Finally, a numerical example is ~iven to show the effectiveness and advantages of the proposed techniques.