Mathematical Problems in Engineering
Volume 7 (2001), Issue 5, Pages 455-484

Passivity analysis and synthesis for uncertain time-delay systems

Magdi S. Mahmoud1 and Lihua Xie2

1Faculty of Engineering, MSA University Amer Street, Mesaha Square, Dokki, Egypt
2School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore

Received 3 October 2000; Revised 1 March 2001

Copyright © 2001 Magdi S. Mahmoud and Lihua Xie. 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.


In this paper, we investigate the robust passivity analysis and synthesis problems for a class of uncertain time-delay systems. This class of systems arises in the modelling effort of studying water quality constituents in fresh stream. For the analysis problem, we derive a sufficient condition for which the uncertain time-delay system is robustly stable and strictly passive for all admissible uncertainties. The condition is given in terms of a linear matrix inequality. Both the delay-independent and delay-dependent cases are considered. For the synthesis problem, we propose an observer-based design method which guarantees that the closed-loop uncertain time-delay system is stable and strictly passive for all admissible uncertainties. Several examples are worked out to illustrate the developed theory.