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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。
Discusses the stability of continuous positive linear systems switching with average dwell time. Switching system stability is an important part of switching system research. In many practical applications, the stability of a switching system directly determines the performance of the system. If the system’s switching rules are arbitrary, then the system performance will be better. However, for a linear switched positive system, there must be a positive residual Lyapunov function in order to stabilize the system, and the derivative of the function is negative along the system trajectory. Therefore, we first give the definition of Yu Zheng Lyapunov function, and then combine the knowledge of linear matrix inequality to find the differential of Yu Zheng Lyapunov function. Applying some properties of linear switching positive system, we obtain the necessary and sufficient conditions for the system to be stable under the switching of average dwell time for linear switching systems. Finally, a numerical example verifies the validity of the problem.