Feedback stabilization via designed planar centre manifold | Zendy

Dong Yali | Zendy; Cheng Daizhan | Zendy; Qin Huashu | Zendy

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Feedback stabilization via designed planar centre manifold

Author(s) -

Dong Yali,

Cheng Daizhan,

Qin Huashu

Publication year - 2003

Publication title -

international journal of robust and nonlinear control

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.361

H-Index - 106

eISSN - 1099-1239

pISSN - 1049-8923

DOI - 10.1002/rnc.862

Subject(s) - planar , manifold (fluid mechanics) , nonlinear system , multiplicity (mathematics) , eigenvalues and eigenvectors , center manifold , zero (linguistics) , class (philosophy) , control theory (sociology) , mathematics , invariant manifold , feedback control , topology (electrical circuits) , pure mathematics , mathematical analysis , computer science , control (management) , engineering , physics , control engineering , combinatorics , bifurcation , artificial intelligence , mechanical engineering , linguistics , philosophy , computer graphics (images) , hopf bifurcation , quantum mechanics

This paper addresses the problem of local state feedback stabilization of a class of nonlinear systems, which have planar centre manifold. A new technique for designing centre manifold has been developed. Using this approach, a sufficient condition for stabilization of a class of nonlinear system is obtained. The approach has been specified for two particular critical cases: ‘zero centre’ with zero eigenvalue of multiplicity 2 and ‘oscillatory centre’ with a pair of pure imaginary eigenvalues. The control law, which stabilizes the overall system, is also presented. Some examples are presented to indicate how the present theorem may be implemented. Copyright © 2003 John Wiley & Sons, Ltd.

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