Asymptotic Lyapunov stability with probability one of Duffing oscillator subject to time-delayed feedback control and bounded noise excitation
First, the authors express the time-delayed feedback control force in terms of system variables without time delay by using generalized harmonic functions. Then, by using the stochastic averaging method, the obtained differential equations are transformed into Itô stochastic differential equations. The asymptotic Lyapunov stability of the system is studied by means of the Lyapunov exponent. The comparison of analytical results with numerical simulations show that the presented procedure yields accurate results when the time delay is less than one averaged period. It is also shown that the time delay in feedback control can destabilize the system.
scientific article; zbMATH DE number 5620336