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Abstract
A new problem called the disturbance decoupling problem with dynamic feedback (DDPDF) is studied. In the linear case DDPDF is equivalent to the well-known DDP (disturbance decoupling problem), but for a non-linear control system they are essentially different. The disturbance decoupling problem with feedforward is also solved by dynamic feedbacks for non-linear systems. The sufficient and necessary conditions of solvabilities for DDPDF and DDPDF with feedforward are advanced. The results are computable, and we give several examples to explain them.