This paper presents the design and implementation of robust control schemes for two applications of a nanopositioning stage (1) reference trajectory tracking with high resolution over a given bandwidth (2) control design for repetitive motions. The stage has a low degree of freedom monolithic parallel kinematic mechanism using flexure hinges. It is driven by piezoelectric actuators and its displacement is detected by capacitance gauges. The design has strongly coupled dynamics with each actuator input producing in multi-axis motions. The nano-positioner is modeled as a multiple input and multiple output (MIMO) system, and the MIMO plant model is identified by time-domain identification methods. The design of the nano-positioner relies heavily on the control design to account for the high coupling in the system. The proposed H∞ MIMO controller achieves a good performance in terms of resolution, bandwidth and robustness to the modeling uncertainty. In the second part of the paper, we present control design for tasks that require repetitive motion of nano positioning system. These tasks are quite common in micro/nano manipulation and manufacturing. This paper presents a robust control design that gives a significant (over thirty fold) improvement in tracking of repetitive motions on a prespecified frequency band. This design, unlike other schemes, is robust to modeling uncertainties that arise in flexure based mechanisms, and does not require any learning steps during its real time implementation. This design scheme is implemented on a parallel-kinematics XYZ nano positioning stage for repetitive nano-manipulation and nano-manufacturing applications.