Mathematical Problems in Engineering 
Volume 5 (1999), Issue 2, Pages 121-137
doi:10.1155/S1024123X99001027

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

Abstract

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.