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IMA Journal of Mathematical Control and Information Advance Access originally published online on June 8, 2007
IMA Journal of Mathematical Control and Information 2008 25(2):141-156; doi:10.1093/imamci/dnm012
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© The author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Resilient feedback stabilization of discrete-time systems with delays

Magdi S. Mahmoud{dagger}

C-Group Hi-Tech Consultants, PO Box 293, Orman-Dokki, Giza, Egypt

El-Kébir Boukas

Mechanical Engineering Department, Ecole Polytechnique de Montreal, PO Box 6079, Station CV, Montreal, Quebec H3C 3A7, Canada

Peng Shi{ddagger}

Department of Statistics, School of Technology, University of Glamorgan, Pontypridd, Wales CF 37 1DL, UK

{dagger} Email: magdim{at}yahoo.com

{ddagger} Email: pshi{at}glam.ac.uk

Received on August 11, 2006; Revision received March 4, 2007. Accepted on March 19, 2007

A class of linear, uncertain discrete-time systems with state delay is considered. We develop an linear matrix inequality (LMI)-based analysis and redesign procedures for improved robust stability of discrete-time systems with state delay and bounded nonlinearities. Then, we address the robust stabilization using nominal and resilient feedback designs. In both cases, the trade-off between the size of the controller gains and the bounding factors is illuminated and incorporated into the design formalism. Seeking computational convenience, all the developed results are cast in the format of LMIs and several numerical examples are presented throughout the paper.

Keywords: nonlinear systems; time-delay systems; robust stability; resilient control; LMIs.


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