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— In this paper we establish conditions to control the Hopf bifurcation of nonlinear systems with two uncontrollable modes on the imaginary axis. We use the center manifold to reduce the system dynamics to dimension two, and find expressions in terms of the original vector fields.
Necessary conditions for the controllability on linear systems with positive control are presented. The real case is analyzed and the Jordan form representation is employed. The minimum number of necessary controls to obtain controllability is remarked.
In this paper the first Lyapunov coefficient of the emerging periodic solution in the Hopf bifurcation is established. A change of coordinates is introduced to eliminate some quadratic and cubic terms in the dynamic equations and the center manifold theory is used to reduce the dynamics to dimension two.
The influence of the normalized load and the rotor time constant mismatch on the dynam-ical behavior of induction motors under indirect field oriented control (IFOC) is analyzed. We focus the analysis on the Takens-Bogdanov bifurcation using a recent generalization of the Takens-Bogdanov bifurcation Theorem. We have found a criterion that allows us to… (More)