ISBN 978-3-8439-2839-7

978-3-8439-2839-7, Reihe Mathematik

Luc N. Muhirwa
Model Order Reduction of Linear Time Delay Systems

207 Seiten, Dissertation Technische Universität Kaiserslautern (2016), Softcover, A5

Zusammenfassung / Abstract

In this dissertation, systems with delays, particularly linear time delay systems (TDS), are investigated. To this end,

(i) the relationship of the transient motions of the system's output signal in conjunction with the system's transfer function and

(ii) Model order reduction (MOR) of linear TDS

are studied in this work.

Although linear TDS belong to a class of infinite dimensional linear systems, similar to finite dimensional linear systems, linear TDS can be represented by a transfer function.

In the first part of the thesis, we consider functions in time and frequency domain and we show the relation of the occurrence of real zeros of the functions in the frequency domain to the number of zero crossings, overshoot and initial undershoot in the time domain. This relation is then used to obtain new simple ways of proving known results that hold for finite dimensional linear systems and for various generalizations, most notably, for linear TDS.

In the second part of the thesis, MOR of linear TDS is investigated.

A new expansion of the transfer function is introduced which allows for defining the sub-moments of the transfer function. Based on the sub-moment, we present two new MOR techniques, namely, the sub-moment matching method which is a structure preserving technique, and the modified sub-moment matching method which constructs a reduced order system with output delays. Reduced systems obtained by either method match the sub-moments of the transfer function of the original system independent of the delay constants. Moreover, a relationship between the sub-moments of the transfer function and the algebraic condition for the system to be Rn-controllable is also illustrated.

The two approaches presented are also applied to MOR of linear discrete TDS.