Stabilization of nonlinear systems via designed center manifold

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	Stabilization of nonlinear systems via designed center manifold
	Cheng, DZ ; Martin, C
	2001-09-01
发表期刊	IEEE TRANSACTIONS ON AUTOMATIC CONTROL
ISSN	0018-9286
卷号	46 期号:9 页码:1372-1383
摘要	This paper addresses the problem of the local state feedback stabilization of a class of nonlinear systems with nonminimum phase zero dynamics. A new technique, namely, the Lyapunov function with homogeneous derivative along solution curves has been developed to test the approximate stability of the dynamics on the center manifold. A set of convenient sufficient conditions are provided to test the negativity of the homogeneous derivatives. Using these conditions and assuming the zero dynamics has stable and center linear parts, a method is proposed to design controls such that the dynamics on the designed center manifold of the closed-loop system is approximately stable. It is proved that using this method, the first variables in each of the integral chains of the linearized part of the system do not affect the approximation order of the dynamics on the center manifold. Based on this fact, the concept of injection degree is proposed. According to different kinds of injection degrees certain sufficient conditions are obtained for the stabilizability of the nonminimum phase zero dynamics. Corresponding formulas are presented for the design of controls.
关键词	approximate stability center manifold injection degree Lyapunov function with homogeneous derivative zero dynamics
语种	英语
WOS研究方向	Automation & Control Systems ; Engineering
WOS类目	Automation & Control Systems ; Engineering, Electrical & Electronic
WOS记录号	WOS:000170926500003
出版者	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/16425
专题	中国科学院数学与系统科学研究院
通讯作者	Cheng, DZ
作者单位	1.Chinese Acad Sci, Inst Syst Sci, Beijing 100080, Peoples R China 2.Texas Tech Univ, Dept Math & Stat, Lubbock, TX 79409 USA
推荐引用方式 GB/T 7714	Cheng, DZ,Martin, C. Stabilization of nonlinear systems via designed center manifold[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL,2001,46(9):1372-1383.
APA	Cheng, DZ,&Martin, C.(2001).Stabilization of nonlinear systems via designed center manifold.IEEE TRANSACTIONS ON AUTOMATIC CONTROL,46(9),1372-1383.
MLA	Cheng, DZ,et al."Stabilization of nonlinear systems via designed center manifold".IEEE TRANSACTIONS ON AUTOMATIC CONTROL 46.9(2001):1372-1383.