D-stability of polynomial matrices

Necessary and sufficient conditions are formulated for the zeros of an arbi trary polynomial matrix to belong to a given region D of the complex plane. The conditions stem from a general optimization methodology mixing quadrat ic and semidefinite programming, LFRs and rank-one LMIs. They are expressed as an LMI feasibility problem that can be tackled with widespread powerful interior-point methods. Most importantly, the D-stability conditions can b e combined with other LMI conditions arising in robust stability analysis.