There has been a growing interest in the generation and storage of power from ambient vibration using piezoelectric transduction. It is well-known that by connecting a piezoelectric energy harvester to a power-electronic switching network, proper switching control can yield favorable energy transduction. It has also been shown that in broadband response, the switching controller maximizing power flow to storage can be solved as an H2 optimal control problem. For extremely small-scale applications, however, the background power necessary to keep a controller online continuously may exceed the average harvested power. In such circumstances, it is necessary to restrict feedback controllers to a class which can be realized with very little power. This paper investigates the use of passive networks to impose transducer voltage feedback laws on energy harvesting systems. Such an implementation requires external power only to gate one mosfet in the power-electronic drive circuitry at a constant duty cycle. The optimization of the passive network for optimal power generation is a challenging, nonconvex problem. This paper presents some preliminary results on a sub-optimal LMI-based design approach for this problem. An example is given for a stochastically-excited piezoelectric bimorph beam.