  The invariant ellipsoid method is aimed at minimization of the smallest
invariant and attractive set of a linear control system operating under bounded
external disturbances. This paper extends this technique to a class of the
so-called generalized homogeneous system by defining the $\dn-$homogeneous
invariant/attractive ellipsoid. The generalized homogeneous optimal (in the
sense of invariant ellipsoid) controller allows further improvement of the
control system providing a faster convergence and better precision. Theoretical
results are supported by numerical simulations and experiments.
