Preprint No. MPIMD/10-02

Title: Generalized Tangential Interpolation for Model Reduction of Discrete-Time MIMO Bilinear Systems

Author(s): Peter Benner, Tobias Breiten, Tobias Damm

Email: breiten@mpi-magdeburg.mpg.de

Date: 2010-12-08

Abstract:

In this paper, we discuss a model order reduction method for multiple-input and multiple-output discrete-time bilinear control systems. Similar to the continuous-time case, we will show that a system can be characterized by a series of generalized transfer functions. This will be achieved by a multivariate Z-transform of kernels corresponding to an explicit solution formula for discrete-time systems. We will further address the problem of generalized tangential interpolation which naturally comes along with this approach. We will introduce a reasonable generalization of the linear H2-norm. Based on this concept, we discuss the choice of interpolation points. Furthermore, an efficient discretization of continuous-time systems is provided. The performance of the proposed method is evaluated by means of some numerical examples and compared with the method of balanced truncation for bilinear systems.

BibTeX:

@TECHREPORT{MPIMD10-02,
author = {Peter Benner and Tobias Breiten and Tobias Damm},
title = {Generalized Tangential Interpolation for Model Reduction of Discrete-Time MIMO Bilinear Systems},
number = {MPIMD/10-02},
month = dec,
year = 2010,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}


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