In this paper, we present a method for using linear matrix inequalities (LMIs) to synthesize controller gains for a quadrotor system. The controller is based on approximate feedback linearization and is structured to allow for tuning similar to proportional-integral-derivative (PID) controllers. The synthesis procedure generates suboptimal gains with respect to mixed and performance cost functions and a pole placement region constraint. The basic procedure is extended to account for dynamic external disturbances, inexact nonlinearity cancellation, multiplicative actuator uncertainty, and saturated integrators in the control loop. The controller is tested in a real-world flight using 10 Hz position updates with 2 cm standard deviation noise to approximate GPS or vision-based control scenarios.Note to Practitioners-This paper was motivated by the desire for a practical control algorithm for quadrotor unmanned aerial vehicles. While many examples of controllers with strong stability and/or performance guarantees exist, these controllers have limited application due to complicated control structures making adjustment in the field difficult. PID controllers, however, can be simply tuned but lack stability or performance guarantees. The controller we present is similar to PID controllers with respect to ease of tuning, but also has a mathematical foundation for determining gains to give guaranteed performance in uncertain environments. The controller is tested to demonstrate performance in a lab environment with position updates limited to 10 Hz and 2 cm standard deviation noise added to approximate GPS or vision-based control scenarios.