Nonlinear adaptive controller with integral action

This note reveals a new significant property of the adaptive controller design technique proposed by Krstic, Kanellakopoulos and Kokotovic (1994). Namely, it is shown that with the use of special plant model parametrization the standard backstepping design results in an adaptive controller with integral action. The latter means that the controller completely rejects constant input disturbances. It is shown that the revealed property can be extended to nonlinear and nonadaptive cases.