Title :
A Lower Bound for the Balanced Truncation Error for MIMO Systems
Author :
Opmeer, Mark R. ; Reis, Timo
Author_Institution :
Dept. of Math. Sci., Univ. of Bath, Bath, UK
Abstract :
We show that for a class of systems which includes state space symmetric systems, the balanced truncation error is bounded from below by twice the sum of the tail of the Hankel singular values (including multiplicities) divided by the dimension of the input space.
Keywords :
MIMO systems; state-space methods; Hankel singular values; MIMO systems; balanced truncation error; multiplicities; state space symmetric systems; Approximation methods; Capacitance; Eigenvalues and eigenfunctions; Integrated circuit modeling; Observability; Transfer functions; Upper bound; Balanced realization; Hankel operator; balanced realization; balanced truncation; error bound; linear time-invariant systems; linear time-invariant systems.; model reduction;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2014.2368232
