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.