Stabilization of nonlinear systems in compound critical cases

Der-Cherng Liaw, Chun Hone Chen

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


In this paper, we study the stabilization of nonlinear systems in critical cases by using the center manifold reduction technique. Three degenerate cases are considered, wherein the linearized model of the system has two zero eigenvalues, one zero eigenvalue and a pair of nonzero pure imaginary eigenvalues, or two distinct pairs of nonzero pure imaginary eigenvalues; while the remaining eigenvalues are stable. Using a local nonlinear mapping (normal form reduction) and Liapunov stability criteria, one can obtain the stability conditions for the degenerate reduced models in terms of the original system dynamics. The stabilizing control laws, in linear and/or nonlinear feedback forms, are then designed for both linearly controllable and linearly uncontrollable cases. The normal form transformations obtained in this paper have been verified by using code MACSYMA.

Original languageEnglish
Pages (from-to)317-360
Number of pages44
JournalApplied Mathematics and Computation
Issue number2-3
StatePublished - 15 Aug 2002


  • Center manifold reduction
  • Nonlinear systems
  • Stabilization

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