This paper introduces specific extension of model predictive control (MPC) with reference anisotropic control (H_a control) for a robot motion with disturbed measured outputs. The purpose is to exploit advance of flexible multi-step MPC and stabilizing (robust) properties of H_a control serving for disturbance attenuation of disturbed measured outputs. The linking of MPC and H_a control is derived both as a simple improvement of MPC by H_a control providing disturbance attenuation only and as a modification of a cost function in MPC design by an additional tunable term weighting the proximity of MPC design to H_a control. Considered novel H_a control represents adjustable transition between H_2 and H_inf control i.e. between excited (trusting) and too conservative design. The proposed concept of control design is based on state-space formulation that run in output feedback configuration complemented by state estimation based on anisotropic theory again. The theoretical contributions are demonstrated by simulations using a state-space model of robot dynamics of one specific over-actuated planar parallel kinematic machine.