The overall seismic structural design problem, for a given structure, may be considered in terms of its transfer function from the ground motion input to the response output. In this regard, it is the transfer function infimum, or the greatest lower bound, over all possible ground motions that is of interest, as it defines the maximum structural response to any ground motion. More importantly, this infimum value can change over time as damage occurs, and tracking it in real-time would provide significant health monitoring information. However, determining this value, especially for large or complex models, is computationally intense and numerically very ill-conditioned. This research presents a highly efficient, stable and computationally rapid method for determining the seismic transfer function infimum for any structural model undergoing a ground motion. This method is based on the Routh-Hurwitz criterion and provides a simple semi-analytical approach, enabling real-time computation for a given model