This article presents an approach to efficiently control grippers/multifingered hands for dexterous manipulation according to a task, i.e., a predefined trajectory in the object space. The object motion is decomposed using a basis of predefined object motions equivalent to object-level coordinate couplings and leading to the definition of the task-level space. In the proposed approach, the decomposition of the motion in the task space is associated with a robust control design based on linear matrix inequalities (LMIs) and bilinear matrix inequalities (BMIs). Eigenvalue placement ensures the robustness of the system to geometric uncertainties and eigenvector placement decouples the system according to task specifications. A practical evaluation of the proposed control strategy is provided with a two-fingers' and six degrees-of-freedom robotic system manipulating an object in the horizontal plane. Results show a better trajectory tracking and the robustness of the control law according to geometric uncertainties and the manipulation of various objects.