Design of Center Manifold

Daizhan Cheng (), Xiaoming Hu () and Tielong Shen ()
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Daizhan Cheng: Chinese Academy of Sciences, Academy of Mathematics & Systems Science
Xiaoming Hu: Royal Institute of Technology, Optimization and Systems Theory
Tielong Shen: Sophia University, Department of Engineering and Applied Sciences

Chapter Chapter 11 in Analysis and Design of Nonlinear Control Systems, 2010, pp 315-354 from Springer

Abstract: Abstract This chapter provides a systematic technique for designing center manifold of closed loop of nonlinear systems to stabilize the system. The method was firstly presented in [6]. Section 11.1 introduces some fundamental concepts and results about center manifold theory. Section 11.2 considers the case when the zero dynamics has minimum phase. A powerful tool, called the Lyapunov function with homogeneous derivative, is developed in Section 11.3. Section 11.4 and Section 11.5 consider the stabilization of systems with zero center and oscillatory center respectively. The application to generalized normal form is considered in Section 11.6. Section 11.7 is for the stabilization of general control systems.

Keywords: Normal Form; Lyapunov Function; State Feedback; Center Manifold; Zero Dynamic (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-3-642-11550-9_11

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