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IMA Journal of Mathematical Control and Information Advance Access published online on August 2, 2006
IMA Journal of Mathematical Control and Information, doi:10.1093/imamci/dnl021
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© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Article

Analysis and synthesis of uncertain switched discrete-time systems

Magdi S. Mahmoud 1 *, Mohamed N. Nounou 2, and Hazem N. Nounou 3

1 C-Group Hi-Tech Consultants, Dokki-Giza, Egypt
2 Department of Chemical Engineering, UAE University, PO Box 17555, Al-Ain, United Arab Emirates
3 Department of Electrical Engineering, UAE University, PO Box 17555, Al-Ain, United Arab Emirates

* To whom correspondence should be addressed.
Magdi S. Mahmoud, E-mail: magdim{at}yahoo.com


  Abstract

The problems of {Lscript}2 -gain analysis and control synthesis for a class of linear discrete-time switched systems with convex-bounded parameter uncertainties in all system matrices are investigated. The main thrust is based on the constructive use of an appropriate switched Lyapunov functional. The {Lscript}2-gain analysis is to characterize conditions under which the linear switched system with polytopic uncertainties is uniformly quadratically stable with an {Lscript}2 gain smaller than a prescribed constant level. The control synthesis is to design switched feedback schemes, whether based on state-, output measurements or by using dynamic output feedback, to guarantee that the corresponding closed-loop system enjoys the uniform quadratic stability with an {Lscript}2 gain smaller than a prescribed constant level. All the developed results are expressed in terms of convex optimization over linear matrix inequalities and tested on representative examples.

Keywords: switched systems; uniform quadratic stability; switched state feedback; switched output feedback; polytopic uncertainty; LMIs.
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