Design of linear dynamical controllers with D-stability constraints

The paper addresses the problem of the closed-loop eigenvalue clustering for discrete-time linear systems under control of the dynamic controllers. Sufficient design conditions are outlined combining the set of linear matrix inequalities and one linear matrix equality for prescribed D-stable region given by the ellipse in the open unit disc. In addition it is proven that by eliminating the tuning parameter the eigenvalue cluster reduces to the standard D-circle stability region. The validity and applicability of the proposed approach are illustrated by a numerical example.