Efficient solution of large scale Lyapunov and Riccati equations arising in model order reduction problems

Model order reduction of large–scale linear time–invariant systems is an omnipresent task in control and simulation of complex dynamical processes. The solution of large scale Lyapunov and Riccati equations is a major task, e.g., in balanced truncation and related model order reduction methods, in particular when applied to semi–discretized partial differential equations constraint control problems. The software package LyaPack has shown to be a valuable tool in the task of solving these equations since its introduction in 2000. Here we want to discuss recent improvements and extensions of the underlying algorithms and their implementation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)