Ways to achieve the integral control:

q 1. Introduce an
integral in the performance weight *W**e*:

Now if the norm (2-norm or *¥*-norm) between *w* and *z*1 is finite, then *K *must have a pole at s = 0 which is the zero of the sensitivity function.

The standard *H**2* (or *H**¥*) control theory can not be applied to this problem formulation directly
because the pole of s =0 of *W**e* becomes an
uncontrollable pole of the feedback system (A1 is violated).

Suppose *W**e** *can be factorized as follows