Abstract: Robust D-stability problem is studied for affine polynomial matrices that depend affinely on uncertain parameters. The sufficient condition on robust D-stability test of polynomial matrices is established. Second-order GLMI region in the left-half plane of the complex plane is considered. In terms of multiconvexity and linear matrix inequality, this problem is proved to be equivalent to an LMI feasible problem. Finally, a numerical example is given to illustrate validity of the method.