Recent advances in balancing-related model reduction of passive circuit equations Tatjana Stykel, TU Berlin Design of VLSI circuits with distributed elements is no longer possible without computer simulations that involve numerical solution of differential-algebraic equations. Such equations may have very large state space dimension that makes the analysis and simulations unacceptably time consuming and expensive. In this context, model order reduction is of great importance. We consider passivity-preserving model reduction of circuit equations using the positive real and bounded real balanced truncation methods. These methods are based on balancing the solutions of projected Lur'e and Riccati matrix equations. We also discuss their numerical solution exploiting the underlying structure of circuit equations. --------------------------------------------- Tatjana Stykel Institut fuer Mathematik, MA 4-5 Technische Universitaet Berlin Strasse des 17.Juni 136 10623 Berlin Germany