Disturbance cancellation for linear systems by adaptive internal models

The adaptive disturbance cancellation problem is considered for single-input, single-output, linear systems when the linear exosystem which generates the disturbances to be rejected and/or the reference signals to be tracked is unknown, that is both its order 2r+12r+1 and its parameters {ω1,…,ωr}{ω1,…,ωr} are unknown. The proposed regulator makes use of two observers and contains an adaptive internal model which tunes mm internal parameters on the basis of the output regulation error. It is shown that: if m≥rm≥r, that is the adaptive internal model can reproduce the required input, the regulation error tends exponentially to zero; if m