Nonlinear systems possessing linear symmetry

doi:10.1002/rnc.1125

CSpace > 系统科学研究所

	Nonlinear systems possessing linear symmetry
	Cheng, Daizhan; Yang, Guowu; Xi, Zairong
	2007-01-10
发表期刊	INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
ISSN	1049-8923
卷号	17 期号:1 页码:51-81
摘要	This paper tackles linear symmetries of control systems. Precisely, the symmetry of affine nonlinear systems under the action of a sub-group of general linear group GL(n, R). First of all, the structure of state space (briefly, ss) symmetry group and its Lie algebra for a given system is investigated. Secondly, the structure of systems, which are ss-symmetric under rotations, is revealed. Thirdly, a complete classification of ss-symmetric planar systems is presented. It is shown that for planar systems there are only four classes of systems which are ss-symmetric with respect to four linear groups. Fourthly, a set of algebraic equations are presented, whose solutions provide the Lie algebra of the largest connected ss-symmetry group. Finally, some controllability properties of systems with ss-symmetry group are studied. As an auxiliary tool for computation, the concept and some properties of semi-tensor product of matrices are included. Copyright (C) 2006 John Wiley & Sons, Ltd.
关键词	linear symmetry Lie group Lie algebra control system semi-tensor product of matrices
DOI	10.1002/rnc.1125
语种	英语
WOS研究方向	Automation & Control Systems ; Engineering ; Mathematics
WOS类目	Automation & Control Systems ; Engineering, Electrical & Electronic ; Mathematics, Applied
WOS记录号	WOS:000243039900003
出版者	WILEY-BLACKWELL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/4005
专题	系统科学研究所
通讯作者	Cheng, Daizhan
作者单位	Chinese Acad Sci, Inst Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Cheng, Daizhan,Yang, Guowu,Xi, Zairong. Nonlinear systems possessing linear symmetry[J]. INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL,2007,17(1):51-81.
APA	Cheng, Daizhan,Yang, Guowu,&Xi, Zairong.(2007).Nonlinear systems possessing linear symmetry.INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL,17(1),51-81.
MLA	Cheng, Daizhan,et al."Nonlinear systems possessing linear symmetry".INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 17.1(2007):51-81.