Convergence and stability of the robust state estimator obtained in [6] is reinvestigated in this technical note. Some new relations have been established for matrix updates in the recursive state estimation. It is proved that under certain stabilizability and detectability conditions, this robust estimator converges to a stable time invariant system, provided that plant nominal parameters are time invariant and the filter design parameter is fixed. These results are consistent with existent ones, but different from them at the point that there are no orthogonality constraints on uncertainty related system matrices, and therefore widen theoretical guarantees for the effectiveness of the estimation procedure.