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The model reduction method introduced in [Benner, P. and Schneider, A.; Balanced Truncation Model Order Reduction for LTI Systems with many Inputs or Outputs, in A. Edelmayer: Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems, 2010, ISBN/ISSN: 978-963-311-370-7] shows how to reduce linear time-invariant (LTI) continuous-time state space systems with either many inputs or many outputs using the well-known balanced truncation approach. We call this method balanced truncation for many terminals (BTMT). In this work we generalize BTMT to descriptor systems of the form
Eẋ(t) = Ax(t) + Bu(t), A, E ∈ ℝ^{n×n},B ∈ ℝ^{n×m}
y(t) = Cx(t) + Du(t), C ∈ ℝ^{p×n}, D∈ ℝ^{p×m},
where m ∈ 𝒪(n) and p ≪ n, or vice versa. We show how to obtain a reduced order model by solving one Lyapunov equation and using the Gauss-Kronrod quadrature to compute the needed projection matrices. In particular, we discuss the case when E is singular and show numerical results.
The cluster is supporting the work of all research groups at the institute. With its help many experiments and molecules can be simulated that would not have been doable on a standard workstation, or that would have require unacceptable execution times. The research group Computational Methods in Systems and Control Theory that is in charge of the device, is using the cluster to develop parallel numerical algorithms for model reduction and optimal control.