Mathematical Problems in Engineering
Volume 4 (1998), Issue 2, Pages 165-185

Robust stability and stabilization of a class of uncertain nonlinear systems with delays

Magdi S. Mahmoud

Dept. of Electrical and Computer Engineering, Kuwait University, PO Box 5969, Safat 13060, Kuwait

Received 4 March 1996; Revised 18 October 1996

Copyright © 1998 Magdi S. Mahmoud. 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.


A class of nonlinear systems with norm-bounded uncertainties and state-delay is considered. Two criteria are developed for the robust stability analysis: one is delay-independent and the other is delay-dependent. Methods for robust feedback synthesis are then examined. It is established that linear memoryless controllers are capable of guaranteeing the delay-dependent and delay-independent stabilizability of the closed-loop systems. All the results are expressed in the form of linear matrix inequalities which can be solved by efficient and numerically-stable routines. The developed theory is applied to the stability robustness problem of an industrial jacketed continuous stirred tank reactor.