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Feedback Stabilization of SteadyState and Hopf Bifurcations 
Abstract 
In this paper we consider nonlinear system … In this paper we consider nonlinear systems with steadystate or Hopf bifurcations for
which the bifurcated modes are linearly uncontrollable. The goal is to find state
feedbacks such that the bifurcation for the closed loop system is supercritical, and at
the same time, the linearly controllable subsystem is asymptotically stable. Necessary and
sufficient conditions for the nonexistence of sufficiently smooth state feedbacks have
been obtained under certain nondegeneracy conditions. For the cases when those conditions
are not satisfied, we give explicit constructions of the feedbacks. The construction has
the following separation property: for any linear state feedback such that the
controllable subsystem is asymptotically stable, we could construct gains in the nonlinear
state feedbacks such that the closed loop system is asymptotically stable at the
bifurcation point. totically stable at the
bifurcation point. +


Authors  Yong Wang and Richard Murray + 
ID  1998e + 
Source  1998 Conference on Decision and Control + 
Tag  wm98acdc + 
Title  Feedback Stabilization of SteadyState and Hopf Bifurcations + 
Type  Conference Paper + 
Categories  Papers 
Modification date This property is a special property in this wiki.

15 May 2016 06:19:46 + 
URL This property is a special property in this wiki.

http://www.cds.caltech.edu/~murray/preprints/wm98acdc.pdf + 
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Feedback Stabilization of SteadyState and Hopf Bifurcations +  Title 
