Balance Properties and Stabilization of Min-Max Systems  

作　　者：Yue-Gang Tao Wen-De Chen Yi-Xin Yin 

机构地区：[1]Laboratory of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy of Sciences, Beijing 100080, PRC [2]Laboratory of Systems and Control, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, PRC [3]School of Information Engineering, University of Science and Technology Beijing, Beijing 100083, PRC

出　　处：《International Journal of Automation and computing》2006年第1期76-83,共8页国际自动化与计算杂志（英文版）

基　　金：This work was supported by National Natural Science of China (No.69874040) the National Key Project of China, and the Hundred Talents Program of the Chinese Academy of Sciences.

摘　　要：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 constructive in nature. We provide several examples to demonstrate how the methods work in practice.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 constructive in nature. We provide several examples to demonstrate how the methods work in practice.

关 键 词：BALANCE fixed point min-max systems output feedback structural stabilization. 

分 类 号：N941[自然科学总论—系统科学]