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 ∈ ℝn×n,B ∈ ℝn×m
y(t) = Cx(t) + Du(t), C ∈ ℝp×n, D∈ ℝp×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.