https://murray.cds.caltech.edu/index.php?action=history&feed=atom&title=Feedback_Stabilization_of_Steady-State_and_Hopf_Bifurcations 2026-10-27T23:15:07Z Revision history for this page on the wiki MediaWiki 1.44.2 https://murray.cds.caltech.edu/index.php?title=Feedback_Stabilization_of_Steady-State_and_Hopf_Bifurcations&diff=19993&oldid=prev 2016-05-15T06:19:46Z

<p>htdb2wiki: creating page for 1998e_wm98a-cdc.html</p> <p><b>New page</b></p><div>{{HTDB paper<br /> | authors = Yong Wang and Richard Murray<br /> | title = Feedback Stabilization of Steady-State and Hopf Bifurcations<br /> | source = 1998 Conference on Decision and Control<br /> | year = 1998<br /> | type = Conference Paper<br /> | funding = AFOSR<br /> | url = http://www.cds.caltech.edu/~murray/preprints/wm98a-cdc.pdf<br /> | abstract = In this paper we consider nonlinear systems with steady-state or Hopf bifurcations for<br /> which the bifurcated modes are linearly uncontrollable. The goal is to find state<br /> feedbacks such that the bifurcation for the closed loop system is supercritical, and at<br /> the same time, the linearly controllable subsystem is asymptotically stable. Necessary and<br /> sufficient conditions for the non-existence of sufficiently smooth state feedbacks have<br /> been obtained under certain nondegeneracy conditions. For the cases when those conditions<br /> are not satisfied, we give explicit constructions of the feedbacks. The construction has<br /> the following separation property: for any linear state feedback such that the<br /> controllable subsystem is asymptotically stable, we could construct gains in the nonlinear<br /> state feedbacks such that the closed loop system is asymptotically stable at the<br /> bifurcation point. <br /> | flags = <br /> | tag = wm98a-cdc<br /> | id = 1998e<br /> }}</div>

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