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IMA Journal of Mathematical Control and Information Advance Access originally published online on December 22, 2005
IMA Journal of Mathematical Control and Information 2006 23(2):193-209; 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.

Passivity and passification of jump time-delay systems

Magdi S. Mahmoud**

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

** Email: magdim{at}yahoo.com

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.

Received on 21 April 2004. revised on 24 November 2004. accepted on 5 January 2005.


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