Conference on Decision and Control December 1999
نویسندگان
چکیده
Classi cation of stabilizability via smooth state feedback is obtained for multi input non linear dynamical systems possessing a steady state or Hopf bifurcation with the critical mode being linearly uncontrollable and all other modes being linearly controllable Introduction Much research has been done to analyze the e ects of state feedbacks on the criticality of bi furcations see and the references therein In explicit classi ca tion of stabilizability was obtained under cer tain nondegeneracy conditions for a single in put nonlinear system possessing a steady state or Hopf bifurcation with the critical mode being linearly uncontrollable But one of the key steps in is to put the linear part of the linearly con trollable subsystem into the controller canonical form Since controller canonical forms are not necessarily unique for multi input LTI systems the procedure in might not be applicable to the multi input case In this paper we solve the classi cation of stabilizability for the multi input case without using controller canonical forms The results in and those in this pa per are di erent from the previous research in that they are explicit necessary and su cient conditions Also the stabilizing controllers can be explicitly constructed see Funding for this research was provided in part by AFOSR grant F Steady State Bifurcation Consider the following nonlinear multi input system
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