Table of Contents
Journal of Industrial Engineering
Volume 2013, Article ID 813037, 6 pages
Research Article

PI Controller Design for Time Delay Systems Using an Extension of the Hermite-Biehler Theorem

Unité de Recherche LARA-Automatique, Ecole Nationale d’Ingénieurs de Tunis, BP 37, le Belvédère, 1002 Tunis, Tunisia

Received 14 August 2012; Accepted 10 December 2012

Academic Editor: Alan Chan

Copyright © 2013 Sami Elmadssia et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider stabilizing first-order systems with time delay. The set of all stabilizing proportional-integral PI controllers are determined using an extension of the Hermite-Biehler theorem. The time delay is approximated by a second-order Padé approximation. For uncertain plants, with interval type uncertainty, robust stabilizing PI controllers are determined.