Efficient Approximate Balanced Truncation of General Large-Scale RLC Systems via Krylov Methods

We present an efficient implementation of an approximate balanced truncation model reduction technique for general large-scale RLC systems, described by a statespace model where the C matrix in the time-domain modified nodal analysis (MNA) circuit equation Cx ? ? Gx ? Bu is not necessarily invertible. The large sizes of the models that we consider make most implementations of the balance-and-truncate method impractical from the points of view of computational load and numerical conditioning. This motivates our use of Krylov subspace methods to directly compute approximate lowrank square roots1 of the Gramians of the original system. The approximate low-order general balanced and truncated model can then be constructed directly from these square roots. We demonstrate using three practical circuit examples that our new approach effectively gives approximate balanced and reduced order coordinates with little truncation error.

• Type: Conference
• Year: 2002
• Where: VLSID
• Authors: Q. Su, Venkataramanan Balakrishnan, Cheng-Kok Koh
• Keywords: Approximate Balanced Truncation, Approximate Lowrank Square, Computer Architecture, Little Truncation Error, VLSID 2002