The dual algebraic Riccati equations and the set of all solutions of the discrete-time Riccati equation

doi:10.1080/00207179.2016.1207098

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	The dual algebraic Riccati equations and the set of all solutions of the discrete-time Riccati equation
	Zhang, Liangyin 1; Chen, Michael Z. Q.1; Li, Chanying2
	2017
发表期刊	INTERNATIONAL JOURNAL OF CONTROL
ISSN	0020-7179
卷号	90 期号:7 页码:1371-1388
摘要	In this paper, two new pairs of dual continuous-time algebraic Riccati equations (CAREs) and dual discrete-time algebraic Riccati equations (DAREs) are proposed. The dual DAREs are first studied with some nonsingularity assumptions on the system matrix and the parameter matrix. Then, in the case of singular matrices, a generalised inverse is introduced to deal with the dual DARE problem. These dual AREs can easily lead us to an iterative procedure for finding the anti-stabilising solutions, especially to DARE, by means of that for the stabilising solutions. Furthermore, we provide the counterpart results on the set of all solutions to DARE inspired by the results for CARE. Two examples are presented to illustrate the theoretical results.
关键词	Riccati equation anti-stabilising solution solution set invariant subspace Cayley transform
DOI	10.1080/00207179.2016.1207098
语种	英语
资助项目	National Natural Science Foundation of China[61374053] ; National Natural Science Foundation of China[61422308]
WOS研究方向	Automation & Control Systems
WOS类目	Automation & Control Systems
WOS记录号	WOS:000401710300008
出版者	TAYLOR & FRANCIS LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/25438
专题	系统科学研究所
通讯作者	Chen, Michael Z. Q.
作者单位	1.Univ Hong Kong, Dept Mech Engn, Hong Kong, Hong Kong, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Liangyin,Chen, Michael Z. Q.,Li, Chanying. The dual algebraic Riccati equations and the set of all solutions of the discrete-time Riccati equation[J]. INTERNATIONAL JOURNAL OF CONTROL,2017,90(7):1371-1388.
APA	Zhang, Liangyin,Chen, Michael Z. Q.,&Li, Chanying.(2017).The dual algebraic Riccati equations and the set of all solutions of the discrete-time Riccati equation.INTERNATIONAL JOURNAL OF CONTROL,90(7),1371-1388.
MLA	Zhang, Liangyin,et al."The dual algebraic Riccati equations and the set of all solutions of the discrete-time Riccati equation".INTERNATIONAL JOURNAL OF CONTROL 90.7(2017):1371-1388.