A Geometric Perspective on Bifurcation Control

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Yong Wang and Richard M. Murray
2000 Conference on Decision and Control

In this paper, we analyze the problem of bifurcation control from a

 geometric perspective.  Our goal is to provide coordinate free,
 geometric conditions under which control can be used to alter the
 bifurcation properties of a nonlinear control system.  These
 insights are expected to be useful in understanding the role that
 magnitude and rate limits play in bifurcation control, as well as
 giving deeper understanding of the types of control inputs that are
 required to alter the nonlinear dynamics of bifurcating systems.  We
 also use a model from active control of rotating stall in axial
 compression systems to illustrate the geometric sufficient
 conditions of stabilizability.