We propose a method to control linear time-varying (LTV) discrete-time systems subject to bounded process disturbances and measurable outputs with bounded noise, and polyhedral constraints over system inputs and states. We search over control policies that map the history of measurable outputs to the current control input. We solve the problem in two stages. First, using the original system, we build a linear system that predicts future observations using the past observations. The bounded errors are characterized using zonotopes. Next, we propose control laws based on affine maps of such output prediction errors, and show that controllers can be synthesized using convex linear/quadratic programs. Furthermore, we can add constraints on trajectories and guarantee their satisfaction for all allowable sequences of observation noise and process disturbances. Our method does not require any assumptions about system controllability and observability. The controller design does not directly take into account the state-space dynamics, and its implementation does not require an observer. Instead, partial observability is often sufficient to design a correct controller. We provide the polytopic representation of observability errors and reachable sets in the form of zonotopes. Illustrative examples are included.