1.  Alexandre Seuret and Corentin Briat 
 On the Stability analysis of SampledData Systems with Delays 
 Delays in Networked Control Systems, Advances in Delays and Dynamics, Vol. 6, 2016 

Abstract
BibTeX
The computation of \(\mathscr{H}_2\) and \(\mathscr{H}_{2,\Omega}\) norms for LTI TimeDelay Systems (TDS) are important challenging problems for which several solutions have been provided in the literature. Several of these approaches, however, cannot be applied to systems of large dimension because of the inherent poor scalability of the methods, e.g., LMIs or Lyapunovbased approaches. When it comes to the computation of frequencylimited norms, the problem tends to be even more difficult. In this chapter, a computationally feasible solution using \(\mathscr{H}_2\) model reduction for TDS, based on the ideas provided in Beattie et al. (2012), is proposed. It is notably demonstrates on several examples that the proposed method is suitable for performing both accurate model reduction and norm estimation for largescale TDS.
@incollection{Briat:15ADD1,
author = {A. Seuret and C. Briat and F. Gouaisbaut},
title = {Stability analysis of asynchronous sampleddata systems with discrete timevarying input delay},
booktitle = {Delays in Networked Control Systems},
series = {Advances in Delays and Dynamics},
editor = {A. Seuret and L. Hetel and J. Daafouz and {K.H.} Johansson},
publisher = {SpringerHeidelberg},
isbn = {9783319323718},
pages = {97112},
volume = {6},
year = {2016}
}



2.  Igor Pontes Duff, Pierre Vuillemin, Charles PoussotVassal, Corentin Briat and Cédric Seren 
 Model reduction for norm approximation: An application to largescale timedelay systems 
 Delays in Networked Control Systems, Advances in Delays and Dynamics, Vol. 6, 2016 

Abstract
BibTeX
Controlling a system through a network amounts to solve certain difficulties such as, among others, the consideration of aperiodic sampling schemes and (timevarying) delays. In most of the existing works, delays have been involved in the input channel through which the system is controlled, thereby delaying in a continuous way the control input computed by the controller. We consider here a different setup where the delay acts in a way that the current control input depends on past state samples, possibly including the current one, which is equivalent to considering a discretetime delay, at the sample level, in the feedback loop. An approach based on the combination of a discretetime Lyapunov–Krasovskii functional and a loopedfunctional is proposed and used to obtain tailored stability conditions that explicitly consider the presence of delays and the aperiodic nature of the sampling events. The stability conditions are expressed in terms of linear matrix inequalities and the efficiency of the approach is illustrated on an academic example.
@incollection{Briat:15ADD2,
author = {I. {Pontes Duff} and P. Vuillemin and C. {PoussotVassal} and C. Briat and C. Seren},
title = {Model reduction for norm approximation: An application to largescale timedelay systems},
booktitle = {Delays in Networked Control Systems},
series = {Advances in Delays and Dynamics},
editor = {A. Seuret and L. Hetel and J. Daafouz and {K.H.} Johansson},
publisher = {SpringerHeidelberg},
isbn = {9783319323718},
pages = {3755},
volume = {6},
year = {2016}
}



3.  Corentin Briat, Emre Altug Yavuz and Gunnar Karlsson 
 Impact of propagation delay estimation error on equilibrium and its stability 
 Networking 2011, Lecture Notes in Computer Science, Vol. 6641, pp 356367, 2011 

Abstract
BibTeX
Delaybased transmission control protocols need to separate roundtrip time (RTT) measurements into their constituting parts: the propagation and the queueing delays. We consider two means for this; the ﬁrst is to take the propagation delay as the minimum observed RTT value, and the second is to measure the queueing delay at the routers and feed it back to the sources. We choose FASTTCP as a representative delaybased transmission control protocol for analysis and study the impact of delay knowledge errors on its performance. We have shown that while the ﬁrst method destroys fairness and the uniqueness of the equilibrium, the stability of the protocol can easily be obtained through tuning the protocol terms appropriately. Even though the second technique is shown to preserve fairness and uniqueness of the equilibrium point, we have presented that unavoidable oscillations can occur around the equilibrium point.
@incollection{Briat:11f,
author = {C. Briat and E. A. Yavuz and G. Karlsson},
title = {Impact of Queueing Delay Estimation Error on Equilibrium and Its Stability},
booktitle = {NETWORKING 2011},
series = {Lecture Notes in Computer Science},
editor = {DomingoPascual, Jordi and Manzoni, Pietro and Palazzo, Sergio and Pont, Ana and Scoglio, Caterina},
publisher = {Springer Berlin / Heidelberg},
isbn = {9783642207976},
keyword = {Computer Science},
pages = {356367},
volume = {6641},
url = {http://dx.doi.org/10.1007/9783642207983_27},
year = {2011}
}


