Algorithms for model reduction of large dynamical systems

Three algorithms for the model reduction of large-scale, continuous-time, time-invariant, linear, dynamical systems with a sparse or structured transition matrix and a small number of inputs and outputs are described. They rely on low rank approximations to the controllability and observability Gramians, which can efficiently be computed by ADI based iterative low rank methods. The first two model reduction methods are closely related to the well-known square root method and Schur method, which are balanced truncation techniques. The third method is a heuristic, balancing-free technique. The performance of the model reduction algorithms is studied in numerical experiments.