In this paper, the design of a linear quadratic regulator (LQR) controller for the DC-DC stage of a Solid State Transformer (SST) based on a quad-active-bridge (QAB) to integrate both photovoltaic (PV) power generation and battery energy storage is presented. The gyrator-based average model is used for deriving the state-space representation of the plant. The dynamic performance of the designed controller is verified through extensive simulation of the switching model and validated with experimental results.