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Magdi S. Mahmoud, Passivity and passification of jump time-delay systems, IMA Journal of Mathematical Control and Information, Volume 23, Issue 2, June 2006, Pages 193–209, https://doi.org/10.1093/imamci/dni053
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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.