Finite-time control for systems with multiple disturbances based on adaptive disturbance observer

For a type of nonlinear systems with multiple disturbances, finite-time stability is researched in this paper. The disturbances include unknown frequency disturbance and unknown bounded disturbances. The unknown frequency disturbances are transformed into the model with unknown vectors by Sylvester matrix transformation, which is estimated by designing an adaptive disturbance observer. Then, a finite-time anti-disturbance controller is constructed to keep the system globally stable in finite time. Finally, the validity of the finite-time anti-disturbance controller is proved by simulations, including a numerical example and a satellite attitude control system.