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Dynamic balance depends on proper foot placement in legged locomotion and corresponding placement strategies have mainly been developed using the linear inverted pendulum model as theoretical framework. While this model can identify single leg strategies for balance control, it does not consider the double support that is common to bipedal locomotion, indicating that current strategies do not fully exploit the theoretical potential of balance control in bipedal systems. Here we extend the linear inverted pendulum model to a bipedal system which includes double support dynamics, and derive a reactive balance controller based on foot placement and double stance length. We show that this controller enables the model to stand and walk at user-defined target speeds, to transition between these behaviors by acceleration and deceleration, and to react to intermittent disturbances and compensate for permanent ones, as long as they are compatible with the swing leg dynamics placing the feet. Finally, we discuss how the versatility of this balance controller depends on including double support and suggest further steps to improve dynamic balance control in bipedal systems.