Slowly-varying persistent unmeasured disturbances, i.e. disturbances which allow the process to exhibit quasi steady-state behaviour most of the time, are very common in process-control systems. The inferential control schemes employing the well-known state-reconstruction methods (Luenberger observer, Kalman filter) are unable to cope with such disturbances and have been demonstrated to lead to large errors. The augmentation of the state vector has been proposed as a means for overcoming these difficulties. This paper shows that this procedure yields in general (i.e. always when the number of disturbances exceeds the number of measurements) problems of structural observability and suggests an optimal way to resolve them. As a consequence of this approach a measurement selection criterion is also derived with the objective of minimizing the sensitivity of the state estimates to the disturbances. An interesting parallel is discussed to the dual problem of controllability of a system when the state vector is augmented to allow for integral feedback action.