Reduced-order modeling based on Prony´s and Shank´s methods via the bilinear transformation

In this paper, we propose a new model-order reduction technique for linear dynamic systems. The idea behind this technique is to transform the dynamic system function from the s-domain into the z-domain via the bilinear transformation, then use Prony´s or Shank´s least-squares approximation methods instead of the commonly employed Pade approximation method, and finally transform the reduced system back into the s-domain using the inverse bilinear transformation. Simulation results for large practical systems show that this technique based on Prony´s and Shank´s methods give much higher accuracy than the traditional Pade method. and result in lower-order approximations with negligible increase in simulation time.