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IMA Journal of Mathematical Control and Information Advance Access first published online on August 2, 2006
This version published online on March 22, 2007
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.

Analysis and synthesis of uncertain switched discrete-time systems

Magdi S. Mahmoud{dagger}

C-Group Hi-Tech Consultants, Dokki-Giza, Egypt

Mohamed N. Nounou

Department of Chemical Engineering, Texas A&M University at Qatar, Doha, Qatar

Hazem N. Nounou

Department of Electrical Engineering, Texas A&M University at Qatar, Doha, Qatar

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


  Abstract

The problems of L2-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 L2-gain analysis is to characterize conditions under which the linear switched system with polytopic uncertainties is uniformly quadratically stable with an L2 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 L2 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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