The ability to stabilize and move individual droplets would allow scientists to perform micro-scale manipulation, and unlock the advantages of microfluidics. The challenge lies in the fact that droplet displacements are unstable, and that the system is multi-input-multi-output in nature. This dissertation begins with construction of a state-space model to represents fluid dynamics in a channel network. The model is validated with experimental data, and used to design LQR controllers. The controllers utilize feedback provided from computer vision, to actuate electro-pneumatic transducers appropriately in order to stabilize and control droplet movements. A significant portion of this report is dedicated to describing a custom computer program that was created for implementing the controllers. The program enables users to manipulate droplets in real time by interacting with an augmented video stream. A demonstration is provided in which droplets are generated, stored, merged and split repeatedly on-demand.