Direct adaptive rejection of persistent disturbances (Q1589943)

The paper deals with a system \( x'=Ax+Bu+Gu_d\), \(y= Cx\), where \(u_d\) is a persistent disturbance. It is assumed that the persistent disturbance has a finite representation \(u_d=a_1e_1f_1+\dots +a_le_lf_l\) with \(a_k\) constant scalars, \(e_k\) constant vectors, \(f_k\) functions with \(\|f_k\|=1\). The main result gives conditions when the bounded adaptive gain laws produce asymptotic output tracking. An application to almost periodic disturbances is considered. An illustrative example of the method is given.