Some remarks on Kahler differentials and ordinary differentials in nonlinear control theory

doi:10.1016/j.sysconle.2011.05.006

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	Some remarks on Kahler differentials and ordinary differentials in nonlinear control theory
	Fu, Guofeng 2; Halas, Miroslav 1; Kotta, Uelle 3; Li, Ziming2
	2011-09-01
发表期刊	SYSTEMS & CONTROL LETTERS
ISSN	0167-6911
卷号	60 期号:9 页码:699-703
摘要	In the algebraic approach to nonlinear control systems two similar notions, namely Kahler differentials and the formal vector space of differential one-forms having the properties of ordinary differentials, are frequently used to study the systems. This technical note explains that the formal vector space of differential one-forms is isomorphic to a quotient space (module) of Kahler differentials. These two modules coincide when they are modules over a ring of linear differential operators over the field of algebraic functions. Some remarks and examples demonstrating when the use of Kahler differentials might not be appropriate are included. (C) 2011 Elsevier B.V. All rights reserved.
关键词	Nonlinear systems Algebraic methods Kahler differentials Differential one-forms
DOI	10.1016/j.sysconle.2011.05.006
语种	英语
资助项目	National Natural Science Foundation of China[60821002/F02] ; Slovak Grant Agency[VG-1/0369/10] ; Estonian Science Foundation[8365]
WOS研究方向	Automation & Control Systems ; Operations Research & Management Science
WOS类目	Automation & Control Systems ; Operations Research & Management Science
WOS记录号	WOS:000295251600004
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12305
专题	系统科学研究所
通讯作者	Halas, Miroslav
作者单位	1.Slovak Univ Technol Bratislava, Inst Control & Ind Informat, Fac Elect Engn & IT, Bratislava 81219, Slovakia 2.Chinese Acad Sci, AMSS, Key Lab Math Mechanizat, Beijing 100190, Peoples R China 3.Tallinn Univ Technol, Inst Cybernet, EE-12618 Tallinn, Estonia
推荐引用方式 GB/T 7714	Fu, Guofeng,Halas, Miroslav,Kotta, Uelle,et al. Some remarks on Kahler differentials and ordinary differentials in nonlinear control theory[J]. SYSTEMS & CONTROL LETTERS,2011,60(9):699-703.
APA	Fu, Guofeng,Halas, Miroslav,Kotta, Uelle,&Li, Ziming.(2011).Some remarks on Kahler differentials and ordinary differentials in nonlinear control theory.SYSTEMS & CONTROL LETTERS,60(9),699-703.
MLA	Fu, Guofeng,et al."Some remarks on Kahler differentials and ordinary differentials in nonlinear control theory".SYSTEMS & CONTROL LETTERS 60.9(2011):699-703.