Advances in Radio Science www.adv-radio-sci.net 1684-9965 1684-9973 6 Kleinheubacher Berichte 2007 2008 10.5194/ars-6-129-2008 http://www.adv-radio-sci.net/6/129/2008/ http://www.adv-radio-sci.net/6/129/2008/ars-6-129-2008.html http://www.adv-radio-sci.net/6/129/2008/ars-6-129-2008.pdf 129 132 2008-05-26 Model order reduction of linear time invariant systems Lj. Radić-Weissenfeld S. Ludwig W. Mathis W. John Leibniz University of Hannover, Institute of Electromagnetic Theory, Hannover, Germany Advanced System Engineering (ASE), Fraunhofer Institute for Reliability and Microintegration (IZM), Paderborn, Germany This paper addresses issues related to the order reduction of systems with multiple input/output ports. The order reduction is divided up into two steps. The first step is the standard order reduction method based on the multipoint approximation of system matrices by applying Krylov subspace. The second step is based on the rejection of the weak part of a system. To recognise the weak system part, Lyapunov equations are used. Thus, this paper introduces efficient solutions of the Lyapunov equations for port to port subsystems. Anatoulas, A. C. and Sorensen, D. C.: Approximation of large-scale dynamica systems: An overview, I J A M., 11(5), 1093–1121, 2001. Boley, D. L.: Krylov Space Methods on State-space Control Models, Circ. Syst. Signal Pr., 13(6), 733–758, 1994. Feldmann, P.: Model Order Reduction of Systems with Large Numbers of Terminals, Proceedings of the Design, Automation and Test in Europe Conference and Exhibition, Paris, France, 2, 944-947, 2004. Gstoettner, A., Steinecke T., and Huemer, M.: Activity Based High Level Modeling of Dynamic Switching Currents in Digital IC Modules, EMC Zurich 2006, Singapore, 2006. Li, J.-R., Wang, F. and White, J.: An Efficient Lyapunov Equation-Based Approach for Generating Reduced-Order Models of Interconnect, Proceedings of 36th Design Automation Conference, New Orleans, LA, USA, 1–6, 1999. Ludwig, S., Radić-Weissenfeld, Lj., Mathis, W., and John, W.: Model Order Reduction of Integrated Circuit Conducted Emission Models, Proceedings of the EMC Compo, Torino, Italy, November 2007, 215-219, 2007. Ludwig, S., Radić-Weissenfeld, Lj., Mathis, W., and John, W.: Efficient Network Description of IC Conducted Emission Models for Model Reduction, Adv. Radio Sci., in press, 2008. Silva, J. M., Vilena, J. F., Flores, P., and Miguel, L.: Outstanding Issues in Model Order Reduction, Proceedings of the Scientific Computing in Electrical Engineering, Sinaia, Romania, September 2006, 11, 139-152, 2006. Steinecke, T., Goekcen, M., and Gstoettner, A.: High-Accuracy Eission Simulation Models for VLSI Chips including Package and Printed Circuit Board, EMC Compo 2006, Torino, Italy, 41-46, 2006.