Books

1. Corentin Briat
LPV & Time-Delay Systems - Analysis, Observation, Filtering & Control (ToC, AMS Book Review, Google Books)
Advances in Delay and Dynamics, Vol. 3, Springer-Heidelberg, 2015
Abstract BibTeX
This book provides an introduction to the analysis and control of linear parameter-varying systems and time-delay systems and their interactions. The purpose is to give the readers some fundamental theoretical background on these topics and to give more insights on the possible applications of these theories. This monograph is intended to be self-contained and is written in an accessible way for readers ranging from undergraduate/PhD students to engineers and researchers willing to know more about the fields of time-delay systems, parameter-varying systems, robust analysis, robust control, gain-scheduling techniques in the LPV fashion and LMI-based approaches. The only prerequisites are basic knowledge in linear algebra, ordinary differential equations and (linear) dynamical systems. Most of the results are proved unless the proof is too complex or not necessary for a good understanding of the results. In the latter cases, suitable references are systematically provided.

The first part pertains on the representation, analysis and control of LPV systems along with a reminder on robust analysis and control techniques. The second part is concerned with the representation and analysis of time-delay systems using various time-domain techniques. The third and last part is devoted to the representation, analysis, observation, filtering and control of LPV time-delay systems. The last topic is about the manipulation of LMIs, extensively used in this monograph, for which many basic and advanced results are presented.
@book{BriatBook,
author = "Corentin Briat",
title = "LPV \& Time-Delay Systems -- Analysis, Observation, Filtering \& Control",
publisher="Springer-Heidelberg, Germany",
volume ="3",
year = "2015",
}



Book chapters

1. Alexandre Seuret and Corentin Briat
On the Stability analysis of Sampled-Data 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 Time-Delay 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 Lyapunov-based approaches. When it comes to the computation of frequency-limited 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 large-scale TDS.
@incollection{Briat:15ADD1,
author = {A. Seuret and C. Briat and F. Gouaisbaut},
title = {Stability analysis of asynchronous sampled-data systems with discrete time-varying 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 = {Springer-Heidelberg},
isbn = {978-3-319-32371-8},
pages = {97--112},
volume = {6},
year = {2016}
}


2. Igor Pontes Duff, Pierre Vuillemin, Charles Poussot-Vassal, Corentin Briat and Cédric Seren
Model reduction for norm approximation: An application to large-scale time-delay 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 (time-varying) 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 discrete-time delay, at the sample level, in the feedback loop. An approach based on the combination of a discrete-time Lyapunov–Krasovskii functional and a looped-functional 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. {Poussot-Vassal} and C. Briat and C. Seren},
title = {Model reduction for norm approximation: An application to large-scale time-delay 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 = {Springer-Heidelberg},
isbn = {978-3-319-32371-8},
pages = {37--55},
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 356-367, 2011
Abstract BibTeX
Delay-based transmission control protocols need to separate round-trip 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 FAST-TCP as a representative delay-based 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 = {Domingo-Pascual, Jordi and Manzoni, Pietro and Palazzo, Sergio and Pont, Ana and Scoglio, Caterina},
publisher = {Springer Berlin / Heidelberg},
isbn = {978-3-642-20797-6},
keyword = {Computer Science},
pages = {356-367},
volume = {6641},
url = {http://dx.doi.org/10.1007/978-3-642-20798-3_27},
year = {2011}
}


Theses/Reports

1. Corentin Briat
Robust Control and Observation of LPV Time-Delay Systems (slides)
Ph.D Thesis Manuscript, Grenoble INP, France, 2008
Abstract BibTeX
This thesis deals with the control and observation/filtering of LPV/LTI uncertain time-delay systems with both constant and time-varying delays. At the difference of finite dimensional systems, the derivation of design tools from stability results is more difficult to due a larger number of decision matrices involved in the LMI conditions. This thesis is based on a particular Lyapunov-Krasovskii functional leading to a non-convex condition when used for design objectives. Several types of relaxations are discussed and a relaxation based on the introduction of a \'slack\' variable is considered. This relaxation has the benefit of simplifying the design problem at the expense of increasing (slightly) the conservatism and the computational complexity. Another advantage of this approach is the possibility of generalization to more complex functional such as discretized functionals, leading then to an efficient reduction of conservatism. Using these results, both memory and memoryless controllers/observers have been developed and more precisely controllers implementing inexact delay have been studied leading to the notion of \'delay-robust controllers\'. Moreover, a new type of controllers referred to as \'delay-scheduled controllers\' have also been introduced. In such controllers, the gain is scheduled by the delay-value (as done in the LPV framework) and a robust synthesis with respect to delay uncertainty is performed. The interest of such an approach is to embed an information on the delay in the controller without the necessity of storing past values of the delayed-state (as done for controller with memory). The design of such controllers is difficult and relies on several techniques that need to be improved in future works.
@PHDTHESIS{BriatPhD:08a,
author = "C.~Briat",
title = "Robust Control and Observation of {LPV} Time-Delay Systems",
school = "INP-Grenoble",
year = "2008",
url = "{http://www.briat.info/thesis/PhDThesis.pdf}"
}