This paper presents an interaction control algorithm for a dielectric elastomer (DE) membrane actuator. The proposed method permits to efficiently exploit the controllable stiffness of the material, and use it as a “programmable spring”, thus enhancing its use in applications such as robotic manipulation or haptic devices. To achieve this goal, a design algorithm based on linear matrix inequalities is proposed, which grounds on a framework developed in the authors' previous works. The resulting controller is a low-gain partial state feedback law that controls the elastomer stiffness, while providing robust stability and performance with respect to model nonlinearities. The approach is validated on an experimental prototype consisting of a DE membrane preloaded with a bi-stable biasing spring.