  We generalize the concepts of D-stability and additive D-stability of
matrices. For this, we consider a family of unbounded regions defined in terms
of Linear Matrix Inequalities (so-called LMI regions). We study the problem
when the localization of a matrix spectrum in an unbounded LMI region is
preserved under specific multiplicative and additive perturbations of the
initial matrix. The most well-known particular cases of unbounded LMI regions
(namely, conic sectors and shifted halfplanes) are considered. A new
D-stability criterion as well as sufficient conditions for generalized
D-stability are analyzed. Several applications of the developed theory to
dynamical systems are shown.
