Feedback linearization of the nonlinear control system with disturbance

Feedback linearization of a nonlinear system is to find a nonsingular feedback and a state transformation such that the closed-loop system is linear in the new state coordinates. For the nonlinear control systems with disturbance, the feedback linearization problem is difficult to solve, because we cannot use feedback through disturbance input channel. We define, for the first time, the feedback linearization problem of the nonlinear systems with disturbance and find the verifiable necessary and sufficient conditions. Since our proofs are constructive, a desired state transformation and a feedback can also be found in the theorem.