You are here: MIMS > EPrints
MIMS EPrints

2009.12: A posteriori error bounds for discrete balanced truncation

2009.12: Younes Chahlaoui (2009) A posteriori error bounds for discrete balanced truncation. SIAM Journal on Scientific Computing (SISC).

There is a more recent version of this eprint available. Click here to view it.

Full text available as:

PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
269 Kb


Balanced truncation of discrete linear time-invariant systems is an automatic method once an error tolerance is specified and yields an a priori error bound, which is why it is widely used in engineering for simulation and control. We present some new insight into this method. We derive a discrete version of Antoulas's $\mathcal{H}_2$-norm error formula \cite[p.218]{Ant05} and show how to adapt it to some special cases. This error bound is an a posteriori computable upper bound for the $\mathcal{H}_2$-norm of the error system defined as the system whose transfer function corresponds to the difference between the transfer function of the original system and the transfer function of the reduced system. The main advantage of our results is that we use the information already available in the balanced truncation algorithm in order to compute the $\mathcal{H}_2$-norm instead of computing one gramian of the corresponding error system. There is always a computational restriction on solving high-dimensional Stein equations for gramians. The a posteriori bound gives insight into the quality of the reduced system and can be used to solve many problems accompanying the order reduction operation.

Item Type:Article
Additional Information:


Uncontrolled Keywords:Model reduction, balanced truncation, gramians, Stein equations, $\mathcal{H}_2$-norm.
Subjects:MSC 2000 > 15 Linear and multilinear algebra; matrix theory
MSC 2000 > 37 Dynamical systems and ergodic theory
MSC 2000 > 65 Numerical analysis
MSC 2000 > 93 Systems theory; control
MIMS number:2009.12
Deposited By:Dr Younes Chahlaoui
Deposited On:09 February 2009

Available Versions of this Item

Download Statistics: last 4 weeks
Repository Staff Only: edit this item