This document summarizes a project to stabilize an inverted pendulum using a lead-lag compensator. It includes the mathematical modeling of the inverted pendulum system and motor cart dynamics. The transfer functions of the individual systems and overall plant are derived. Root locus analysis is used to design the compensator. An analog to digital converter and parallel port are used to interface the hardware and send sensor readings to the computer for processing. References on control systems and inverted pendulum simulations are also provided.