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A new control paradigm using angular momentum and foot placement as state variables in the linear inverted pendulum model has expanded the realm of possibilities for the control of bipedal robots. This new paradigm, known as the ALIP model, has shown effectiveness in cases where a robot's center of mass height can be assumed to be constant or near constant as well as in cases where there are no non-kinematic restrictions on foot placement. Walking up and down stairs violates both of these assumptions, where center of mass height varies significantly within a step and the geometry of the stairs restrict the effectiveness of foot placement. In this paper, we explore a variation of the ALIP model that allows the length of the virtual pendulum formed by the robot's stance foot and center of mass to follow smooth trajectories during a step. We couple this model with a control strategy constructed from a novel combination of virtual constraint-based control and a model predictive control algorithm to stabilize a stair climbing gait that does not soley rely on foot placement. Simulations on a 20-degree of freedom model of the Cassie biped in the SimMechanics simulation environment show that the controller is able to achieve periodic gait.