Homogeneous control design using invariant ellipsoid method

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.