Balance Properties and Stabilization of Min-Max Systems

Yue-Gang Tao Wen-De Chen Yi-Xin Yin

Yue-Gang Tao, Wen-De Chen, Yi-Xin Yin. Balance Properties and Stabilization of Min-Max Systems[J]. 国际自动化与计算杂志(英)/International Journal of Automation and Computing, 2006, 3(1): 76-83. doi: 10.1007/s11633-006-0076-y
引用本文: Yue-Gang Tao, Wen-De Chen, Yi-Xin Yin. Balance Properties and Stabilization of Min-Max Systems[J]. 国际自动化与计算杂志(英)/International Journal of Automation and Computing, 2006, 3(1): 76-83. doi: 10.1007/s11633-006-0076-y
Yue-Gang Tao, Wen-De Chen and Yi-Xin Yin. Balance Properties and Stabilization of Min-Max Systems. International Journal of Automation and Computing, vol. 3, no. 1, pp. 76-83, 2006 doi:  10.1007/s11633-006-0076-y
Citation: Yue-Gang Tao, Wen-De Chen and Yi-Xin Yin. Balance Properties and Stabilization of Min-Max Systems. International Journal of Automation and Computing, vol. 3, no. 1, pp. 76-83, 2006 doi:  10.1007/s11633-006-0076-y

Balance Properties and Stabilization of Min-Max Systems

doi: 10.1007/s11633-006-0076-y
基金项目: 

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.

Balance Properties and Stabilization of Min-Max Systems

Funds: 

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.

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出版历程
  • 收稿日期:  2005-03-01
  • 修回日期:  2005-09-15
  • 刊出日期:  2006-01-15

Balance Properties and Stabilization of Min-Max Systems

doi: 10.1007/s11633-006-0076-y
    基金项目:

    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 min, 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.

English Abstract

Yue-Gang Tao, Wen-De Chen, Yi-Xin Yin. Balance Properties and Stabilization of Min-Max Systems[J]. 国际自动化与计算杂志(英)/International Journal of Automation and Computing, 2006, 3(1): 76-83. doi: 10.1007/s11633-006-0076-y
引用本文: Yue-Gang Tao, Wen-De Chen, Yi-Xin Yin. Balance Properties and Stabilization of Min-Max Systems[J]. 国际自动化与计算杂志(英)/International Journal of Automation and Computing, 2006, 3(1): 76-83. doi: 10.1007/s11633-006-0076-y
Yue-Gang Tao, Wen-De Chen and Yi-Xin Yin. Balance Properties and Stabilization of Min-Max Systems. International Journal of Automation and Computing, vol. 3, no. 1, pp. 76-83, 2006 doi:  10.1007/s11633-006-0076-y
Citation: Yue-Gang Tao, Wen-De Chen and Yi-Xin Yin. Balance Properties and Stabilization of Min-Max Systems. International Journal of Automation and Computing, vol. 3, no. 1, pp. 76-83, 2006 doi:  10.1007/s11633-006-0076-y
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