  We introduce a model reduction approach for linear time-invariant second
order systems based on positive real balanced truncation. Our method guarantees
asymptotic stability and passivity of the reduced order model as well as the
positive definiteness of the mass and stiffness matrices. Moreover, we receive
an a priori gap metric error bound. Finally, we show that our method based on
positive real balanced truncation preserves the structure of overdamped second
order systems.
