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Design of Center Manifold

In: Analysis and Design of Nonlinear Control Systems

Author

Listed:
  • 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)

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.

Suggested Citation

  • Daizhan Cheng & Xiaoming Hu & Tielong Shen, 2010. "Design of Center Manifold," Springer Books, in: Analysis and Design of Nonlinear Control Systems, chapter 0, pages 315-354, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11550-9_11
    DOI: 10.1007/978-3-642-11550-9_11
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