In this paper, we consider a multiple-input multiple-output wireless powered communication network (MIMO-WPCN), where multiple users harvest energy from a dedicated power station in order to be able to transmit their information signals to an information receiving station. Employing a practical non-linear energy harvesting (EH) model, we propose a joint time allocation and power control scheme, which takes into account the uncertainty regarding the channel state information (CSI) and provides robustness against imperfect CSI knowledge. In particular, we formulate two non-convex optimization problems for different objectives, namely system sum throughput maximization and maximization of the minimum individual throughput across all wireless powered users. To overcome the non-convexity, we apply several transformations along with a one-dimensional search to obtain an efficient resource allocation algorithm. Numerical results reveal that a significant performance gain can be achieved when the resource allocation is designed based on the adopted non-linear EH model instead of the conventional linear EH model. Besides, unlike a non-robust baseline scheme designed for perfect CSI, the proposed resource allocation schemes are shown to be robust against imperfect CSI knowledge.