Recently, a variety of differential power-processing (DPP) architectures have been shown to improve the efficiency of photovoltaic (PV) systems. This paper proposes a simple control strategy for the isolated-port DPP architecture, and provides a comprehensive stability analysis for this system. The proposed controller drives the duty-cycle of the differential submodule integrated converters (subMICs) in proportion to a voltage difference between the submodule and the isolated-port. This method requires no additional sensing, complex processing, or communication between subMICs, and is therefore well suited for low-cost integrated hardware solutions. Stability of the resulting high-order nonlinear system is analyzed both in the time and frequency domains. A decoupled model is developed that reduces the high-order system dynamics to a 1-D control loop, which allows stable, well-behaved responses using a proportional or a lag compensator. Experimental results for a 72-cell PV module with three subMICs verify static and dynamic operation, and show that overall PV module efficiency exceeds 99% with no shading, and is higher than 96% under significant (50%) shading.