一类不确定区间系统最大摄动界的有限判别方法

北京大学学报（自然科学版）

一类不确定区间系统最大摄动界的有限判别方法

兰轶东, 王龙, 张霖¹

北京大学力学与工程科学系，系统与控制研究中心，北京，100871；¹清华大学CIMS工程研究中心，北京，100084

收稿日期:2002-12-18 出版日期:2004-01-20 发布日期:2004-01-20

The Finite Checking Method of the Largest Stability Bound for a Class of Uncertain Interval Systems

LAN Yidong, WANG Long, ZHANG Lin¹

Department of Mechanics and Engineering Science, Peking University, Beijing, 100871; ¹CIMS Engineering Research Center, Tsinghua University, Beijing, 100084

Received:2002-12-18 Online:2004-01-20 Published:2004-01-20

摘要/Abstract

摘要： 线性区间系统Hurwitz稳定时系数的最大摄动界，利用半保护映射可以经过有限判别求得。含有两个区间参数的多线性区间系统Hurwitz稳定时系数的最大摄动界，同时利用半保护映射和多项式完全判别系统，也可以通过有限判别求得。给出的两个算例说明了方法的有效性。对于含有任意多个区间参数的多线性区间系统，也给出了其系数的最大摄动界的有限判别方法。

关键词: 半保护映射, 多项式完全判别系统, 线性区间系统, 最大摄动界

Abstract: The largest stability bound for linear interval system, by guardian map approach, through finite checking can be obtained. The largest stability bound for multilinear interval system containing two interval coefficients, by guardian map approach and complete discrimination system for polynomials, through finite checking can also be obtained. Two examples illuminate the utility of our methods. For the multilinear system containing n(n>2) interval coefficients, it is also given that the method to compute its largest stability bound through finite checking.

Key words: semi-guardian map, complete discrimination system for polynomials, linear interval system, largest stability bound

中图分类号:

O236
TP14

兰轶东, 王龙, 张霖. 一类不确定区间系统最大摄动界的有限判别方法[J]. 北京大学学报（自然科学版）.

LAN Yidong,WANG Long,ZHANG Lin. The Finite Checking Method of the Largest Stability Bound for a Class of Uncertain Interval Systems[J]. Acta Scientiarum Naturalium Universitatis Pekinensis.

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