Bifurcations of Control Systems: A View from Control Flows

  • Fritz Colonius
  • Wolfgang Kliemann
Part I: Bifurcation and Normal Form
Part of the Lecture Notes in Control and Information Science book series (LNCIS, volume 295)


The purpose of this paper is to discuss bifurcation problems for control systems viewing them as dynamical systems, i.e., as control flows. Here open loop control systems are considered as skew product flows where the shift along the control functions is part of the dynamics. Basic results from this point of view are contained in the monograph [8]. In the present paper we survey recent results on bifurcation problems-some new results are included and a number of open problems is indicated. Pertinent results from [8] are cited if necessary for an understanding.


Normal Form Singular Point Lyapunov Exponent Uncontrolled System Chain Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Authors and Affiliations

  • Fritz Colonius
    • 1
  • Wolfgang Kliemann
    • 2
  1. 1.Institut für Mathematik, Universität Augsburg, 86135 AugsburgGermany
  2. 2.Department of Mathematics, Iowa State University, Ames IA 50011U.S.A

Personalised recommendations