Mathematical Problems in Engineering
Volume 7 (2001), Issue 5, Pages 393-412
doi:10.1155/S1024123X01001703

Robust stability and ℋ∞-estimation for uncertain discrete systems with state-delay

Magdi S. Mahmoud1,2

1Faculty of Engineering, Arab Academy for Science and Technology, PO Box 2033 El Horrya, Helliopolis, Cairo, Egypt
2Department of Electrical and Computer Engineering, Kuwait University, Kuwait

Received 1 December 1999; Revised 30 January 2001

Copyright © 2001 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.

Abstract

In this paper, we investigate the problems of robust stability and ℋ∞-estimation for a class of linear discrete-time systems with time-varying norm-bounded parameter uncertainty and unknown state-delay. We provide complete results for robust stability with prescribed performance measure and establish a version of the discrete Bounded Real Lemma. Then, we design a linear estimator such that the estimation error dynamics is robustly stable with a guaranteed ℋ∞-performance irrespective of the parameteric uncertainties and unknown state delays. A numerical example is worked out to illustrate the developed theory.