We demonstrate the feasibility of linear feedback control to stabilize the vortex shedding behind twin cylinders using cylinder rotation. Our approach is to use linear feedback control theory to stabilize the steady-state solution and apply this control to the nonlinear Navier-Stokes equations. Thus, we linearize the flow about a desired steady-state flow and obtain the Oseen equations, use interpolation-based model reduction on the resulting linear model to generate a low-dimensional model of the input-output system with input-independent error bounds, then use this reduced model to design the feedback control law. We then consider the practical issue of limited state measurements by building a nonlinear compensator that is computed from the same linear reduced-order model and constructed through an extended Kalman filter with a proper orthogonal decomposition (POD) model. Closed-loop simulations of the Navier-Stokes equations coupled with controls generated through flow measurements demonstrate the effectiveness of this control strategy. This is joint work with Serkan Gugercin and Lizette Zietsman.