Model reference adaptive control of system having purely deterministic disturbances

This note presents results relating to the adaptive control of linear time invariant systems having purely deterministic disturbances such as sine waves, biases, etc. Two key points are made. First, it is shown that the usual ARMA model used in adaptive control can also include a description of purely deterministic disturbances. Second, it is shown that the existing convergence theory for adaptive control schemes can be extended in a very straightforward way to the case where disturbances are present.