Efficient Approximate Balanced Truncation of General
Large-Scale RLC Systems via Krylov Methods
Efficient Approximate Balanced Truncation of General
Large-Scale RLC Systems via Krylov Methods
Q. Su, V. Balakrishnan and C-K. Koh
In Proc. ASPDAC/Int. Conf. VLSI Design, pages 311-316,
Bangalore, India,
January 2002
Abstract:
We present an efficient implementation of an approximate balanced
truncation model reduction technique for general large-scale RLC
systems, described by a state-space model where the C matrix in the
time-domain modified nodal analysis (MNA) circuit equation
C xdot = -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 low-rank
square roots 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.
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