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IMA Journal of Mathematical Control and Information Advance Access published online on December 22, 2005
IMA Journal of Mathematical Control and Information, doi:10.1093/imamci/dni053
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© The author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Received April 21, 2004
Revised November 24, 2004
Accepted January 5, 2005

Article

Passivity and passification of jump time-delay systems

Magdi S. Mahmoud 1 *

1 Canadian International College, Al Tagamoa Al Khamis, New Cairo City, Egypt

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


  Abstract

In this paper, the problems of passivity and passification of a class of linear jumping time-delay systems are investigated. The jumping parameters are modelled as a continuous-time, discrete-state Markov process. The interplay between time-delay pattern and passivity concept is examined leading to three distinct cases: passivity with weak delay dependence, passivity with strong delay dependence (PSDD) and passivity with functional time delay. In the case of PSDD, a new state transformation is developed to exhibit the delay dependence. It is established that the passivity conditions can always be cast in a linear matrix inequality format. Complete results on state feedback passification are subsequently developed.

Keywords: jumping time-delay systems; weak delay dependence; strong delay dependence; functional delay dependence; passivity; feedback passification.
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