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The progressive electrification of railways involves an increasing number of power electronic converters connected to the railway catenary, which may compromise its stability. Both the converter for traction and the converter for auxiliary power systems (APS) behave as constant power loads (CPL) and interact negatively with the catenary impedance producing voltage instability. This article applies quantitative feedback theory (QFT) to design an ac voltage controller for the APS converter that shapes the dc input admittance of the converter by performing only ac side-control without a dc-side feedback loop. The QFT enables to design a low order controller that satisfies multiple performance specifications in systems with high uncertainty as is the case of the train system. The proposed control guarantees catenary stability while ensuring ac output voltage reference tracking and providing robustness to unmodeled uncertainties. As an additional contribution, the article presents an algorithm for including input admittance specifications in the QFT design process. The proposed control has been evaluated on an experimental platform that recreates the train system. Experimental results show that the controlled system meets railway standards and correctly shapes the specified dc input impedance.