The saddle-node bifurcation may occur in the frequency response curves in the
cases of primary and superharmonic resonances of a forced single-degree-offreedom
(SDOF) nonlinear system. The appearance of this discontinuous or
catastrophic bifurcation may lead to jump and hysteresis phenomena in the
steady-state response, where at a certain interval of the control parameter, two
stable attractors exit with an unstable one in between. In this paper, a feedback
control law is designed to control the saddle-node bifurcation taking place in
the resonance response, thus removing or delaying the occurrence of jump and
hysteresis phenomena. The structure of feedback control law is determined by
analyzing the eigenvalues of the modulation equations. It is shown that three
types of feedback linear, nonlinear or a combination of linear plus nonlinear
are adequate for the bifurcation control. Also, it is shown by illustrative
examples that the proposed feedback control law is effective for controlling
the primary resonance responses.