This paper investigates control of stick-slip oscillations in drilling from a linear matrix inequality perspective. Stick-slip oscillations include a period of no angular motion at the bit caused by a large static friction torque followed by a period of rapid angular motion at the bit caused by a build up of torque in the drilling pipe. Many of the model parameters are uncertain but belong to convex sets, and the friction torques are not easily modeled. The linear matrix inequality approach facilitates design of state feedback controllers in the presence of polytopic uncertainties and can be optimized to reject disturbance effects relative to outputs. Results indicate that the linear matrix inequality approach leads to a simple controller, successfully alleviates the stick-slip problem, and is robust to uncertainties.

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