Analysis of Harmonically Forced Duffing Oscillator with Time Delay State Feedback by Incremental Harmonic Balance Method

Periodic solutions of a harmonically forced Duffing oscillator with time-delay state feedback are investigated using the incremental harmonic balance method. In process solving, explicit effect matrix time delay term was derived. The stability periodic determined by method which combines continuous approximation and multivariable Floquet theory. On this basis, frequency–amplitude response curve characteristics primary resonance 1/3 subharmonic were obtained. stable results compared obtained numerical method, demonstrated effectiveness accuracy for analysis strongly nonlinear equations delays. influence control parameters on is investigated. periodicity also discussed.