It is demonstrated that robust eigenvalue placement in the disk of an arbitrary radius r centered at -2r can be achieved by a static-state feedback for systems with so-called matched perturbations of uncertain parameters in the state coefficient matrix A (i.e., with perturbations of A in the range of the input matrix B). This implies, in particular, that such systems can be robustly stabilized with an arbitrarily fixed degree of exponential decay, and thus it extends previously known results on robust stabilization without eigenvalue placement conditions. This result is in sharp contrast with the case of general perturbations in either A or B or both, where there are limits for the degree of exponential stabilizability which depend on the size of perturbations.