This technical note firstly presents a sufficient and necessary condition for the robust asymptotical stability of fractional-order interval systems with the fractional order satisfying 0 < alpha < 1. And then a sufficient condition for the robust asymptotical stabilization of such fractional-order interval systems is derived. All the results are obtained in terms of linear matrix inequalities. Finally, two illustrative examples are given to show that our results are effective for checking the robust stability and designing the robust stabilizing controller for fractional-order interval systems.