Approximate dissipative Hamiltonian realization and construction of local Lyapunov functions

doi:10.1016/j.sysconle.2006.08.005

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	Approximate dissipative Hamiltonian realization and construction of local Lyapunov functions
	Wang, Yuzhen ; Cheng, Daizhan ; Ge, S. S.
	2007-02-01
发表期刊	SYSTEMS & CONTROL LETTERS
ISSN	0167-6911
卷号	56 期号:2 页码:141-149
摘要	The key in applying energy-based control approach is to be able to express the system under consideration as a dissipative Hamiltonian system, i.e., to obtain Dissipative Hamiltonian Realization (DHR) for the system. In general, the precise DHR form is hard to obtain for nonlinear dynamic systems. When a precise DHR does not exist for a dynamic system or such a precise realization is difficulty to obtain, it is necessary to consider its approximate realization. This paper investigates approximate DHR and construction of local Lyapunov functions for time-invariant nonlinear systems. It is shown that every nonlinear affine system has an approximate DHR if linearization of the system is controllable. Based on the diagonal normal form of nonlinear dynamic systems, a new algorithm is established for the approximate DHR. Finally, we present the concept of kth degree approximate Lyapunov function, and provide a method to construct such a Lyapunov function. Example studies show that the methodology presented in this paper is very effective. (c) 2006 Elsevier B.V. All rights reserved.
关键词	kth degree approximate DHR kth degree approximate Lyapunov function diagonal normal form algorithm
DOI	10.1016/j.sysconle.2006.08.005
语种	英语
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:000244164300007
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/4596
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Yuzhen
作者单位	1.Shandong Univ, Sch Control Sci & Engn, Jinan 250061, Peoples R China 2.Chinese Acad Sci, Inst Syst Sci, Beijing 100080, Peoples R China 3.Natl Univ Singapore, Dept Elect & Comp Engn, Singapore 117548, Singapore
推荐引用方式 GB/T 7714	Wang, Yuzhen,Cheng, Daizhan,Ge, S. S.. Approximate dissipative Hamiltonian realization and construction of local Lyapunov functions[J]. SYSTEMS & CONTROL LETTERS,2007,56(2):141-149.
APA	Wang, Yuzhen,Cheng, Daizhan,&Ge, S. S..(2007).Approximate dissipative Hamiltonian realization and construction of local Lyapunov functions.SYSTEMS & CONTROL LETTERS,56(2),141-149.
MLA	Wang, Yuzhen,et al."Approximate dissipative Hamiltonian realization and construction of local Lyapunov functions".SYSTEMS & CONTROL LETTERS 56.2(2007):141-149.