In this paper we derive a formulation for Model Predictive Control (MPC) of linear time-invariant systems based on H infinity loop-shaping. The design provides an optimized stability margin for problems that require state estimation. Input and output weights are designed in the frequency domain to satisfy steady-state and transient performance requirements, in lieu of conventional MPC plant model augmentations. The H infinity loop-shaping synthesis results in an observer-based state feedback structure. Using the linear state feedback law, an inverse optimal control problem is solved to design the MPC cost function, and the H infinity state estimator is used to initialize the prediction model at each time step. The MPC inherits the closed-loop performance and stability margin of the loopshaped design when constraints are inactive. We apply the methodology to a multi-zone heat pump system in simulation. The design rejects constant unmeasured disturbances and tracks constant references with zero steady-state error, has good transient performance, provides an excellent stability margin, and enforces input and output constraints.