A note about optimal and suboptimal disturbance rejection

The well-known problem of optimal disturbance re- jection (both in a stochastic framework and in a mean square sense), is addressed by following a Wiener filtering approach. By focusing the analysis to closed loop structures, it is shown that some critical situations may arise, since both the controller causality constraint and the closed loop stability one may prevent the existence of an op- timal controller. When this happens, it is also shown that the mean square infimum value can be approached arbitrarily close by resorting to suitable suboptimal controllers sequences, which agree with both the causality and stability constraints.