Adaptive sinusoidal disturbance cancellation for unknown LTI systems despite input delay

In this paper, the problems of canceling sinusoidal disturbances and compensating input delays in LTI systems are considered simultaneously. The disturbance is parameterized and the delay is represented as a transport PDE. An adaptive controller is designed by using the backstepping boundary control technique for PDEs. It is proven that the equilibrium of the closed loop system is stable and the state of the considered system converges to zero as t → ∞ with perfect disturbance estimation.