Balance Properties and Stabilization of Min-Max Systems

• Published in: International journal of automation and computing Vol. 3; no. 1; pp. 76 - 83
• Main Author: Yue-Gang Tao Wen-De Chen Yi-Xin Yin
• Format: Journal Article
• Language: Chinese
• Published: 2006
• Subjects: 不动点; 平衡性; 最小-最大系统; 稳定性; 输出反馈
• ISSN: 1476-8186; 1751-8520

A variety of problems in operations research, performance analysis, manufacturing, and communication networks, etc., can be modelled as discrete event systems with minimum and maximum constraints. When such systems require only maximum constraints （or dually, only minimum constraints）, they can be studied using linear methods based on max-plus algebra. Systems with mixed constraints are called min-max systems in which rain, max and addition operations appear simultaneously. A significant amount of work on such systems can be seen in literature. In this paper we provide some new results with regard to the balance problem of min-max functions; these are the structure properties of min-max systems. We use these results in the structural stabilization. Our main results are two sufficient conditions for the balance and one sufficient condition for the structural stabilization. The block technique is used to analyse the structure of the systems. The proposed methods, based on directed graph and max-plus algebra are