This paper presents a new control scheme for dexterous manipulation of an object by a multifingered hand. The effects of the uncertainties on the contact orientation and location are investigated and taken into account in the control design, allowing to manipulate the object robustly. The control law has three main objectives: (i) ensuring the motion control of the object, (ii) satisfying the constraints of the manipulation system, and (iii) being robust to the uncertainties on the contact point. The proposed control is based on a state feedback architecture with robust pole placement by an LMI approach. The controller is designed offline and can be related to an object-level impedance controller. The constraints of the manipulation system, e.g. the friction constraints, are taken into account with an additional control action, based on an online LMI evaluation. Simulation results are presented and demonstrate that the proposed control law ensures the three main objectives.