Mathematical Problems in Engineering
Volume 5 (1999), Issue 2, Pages 121-137

Design of delay observer-based controllers for uncertain time-lag systems

Magdi S. Mahmoud and Mohamed Zribi

Department of Electrical and Computer Engineering, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

Received 15 October 1998; Revised 24 February 1999

Copyright © 1999 Magdi S. Mahmoud and Mohamed Zribi. 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, the problem of designing observers and observer-based controllers for a class of uncertain systems with input and state time lags is considered. We construct delay-type observers in which both the instantaneous as well as the delayed measurements are utilized. Using feedback control based on the reconstructed state, the behavior of the closed-loop system is investigated. It is established that the uncertain time-lag system with delay observer-based control is asymptotically stable. Expressions for the gain matrices are given based on two linear-matrix inequalities. A numerical example is given to illustrate the theoretical developments.