Robust finite-time synchronization of chaotic parametrically excited pendulums with multiple uncertainties

Global robust finite-time synchronization of two chaotic parametrically excited pendulums with the parameter mismatches, extern disturbance and time delay is investigated in this paper. Firstly, the robust finite-time synchronization scheme for two chaotic parametrically excited pendulums in the presence of the above three uncertainties is constructed by employing the generalized linear state error feedback control. Then, the global robust finite-time synchronization problem is transformed to the global finite-time stability of the error system originating from the synchronization scheme. Subsequently, a sufficient algebraic criterion for the global robust finite-time synchronization of two parametrically excited pendulums is rigorously proved by using the finite-time stability theory. Also, both the synchronization time and the synchronization error bound are analytically estimated at the same time. Finally, the obtained criterion is verified to be effective by the numerical simulation.