Research activities

Position

Research interests

• Multidimensional (or nD) systems

  I am trying to extend many well-known results of the literature dedicated to LMI, robustness and so on to the realm of nD systems, including the continuous, discrete or hybrid Roesser models, the last ones encompassing the repetitive processes.

  A particular attention has been paid to the Kalman-Yakubovich-Popov (KYP) lemma and other S-procedure-like results.

  The research for sufficient nice and numerically tractable conditions for stabilisability and stabilisation of nD linear models which are close as possible to necessity is a hard but interesting challenge, especially in the 2D case.

  The link between so-called strucutral (or spectral) stability and asymptotic or exponenential stability is particularly studied. We obtained interesting results in the discrete case and aim at further investigating the continuous and mixed continuous-discrete case.

  I am also interested in exploiting the so-called Algebraic analysis approach to the linear systems theory for the specific and peculiar study of 2D models such as Roesser and Fornasini-Marchesini models. This elegant and quite general framework that my mathematician colleagues desperately try to teach me allows to look at the 2D linear models through an original lens. We are particularly interested in the notion of equivalence (in the sense of this approach) to study the possible preservation of structural stability from one model to an equivalent model and to enlarge the set of possibilities for stabilising a 2D model.

  Another subtopic which is dear to me is how to study some PDE's or some chains of connected cells (subsystems) through the lens of nD (for the moment only 2D) systems.

  
  THIS IS THE TOPIC I'M THE MOST INVOLVED IN!
  

• Matrix root-clustering analysis

  I am studying various conditions for the eigenvalues of a matrix (in practice the state matrix of a linear model) to lie in some specified region of the complex plane. This notion is also often referred to as D-stability.
  I am particularly interested in the case where the clustering region is non convex and even non connected (for instance some unions of various subregions, possibly non symmetric with respect to the real axis). For such a purpose, the concepts of DU-stability or dD-regularity of a matrix (which can be generalised to the concept of S-regularity) can reveal as very useful. The necessary and sufficient conditions for D-stability are expressed in terms of linear matrix inequalities (LMI).
  At this time, I am not so involved in this topic... but I can come back to it because it is not unconnected to the previous topic.
  

• Robust matrix root-clustering

  The considered uncertainty is the polytopic or the (norm-bounded) LFT-based uncertainty. It can also be any associations of boths. I aimed at finding sufficient conditions (as tight as possible to necessity) such that a matrix is D-stable with respect to the uncertainty. This leads to the concept of robust D-stability (as well as robust dD-regularity or robust S-regularity).
  At this time, I am not so involved in this topic... but I can come back to it.
  

• Pole placement

  Besides, it is also important to study under which conditions the above-mentioned conditions can be exploited for the design of a control law. Nevertheless, not only the pole placement is some regions is investigated but I am also working on the derivation of some non-iterative techniques to assign strict closed-loop poles by a static output feedback control law, even when the so-called Kimura's condition does not hold. Of course the improvement of the robustness induced by such laws is a challenge.
  At this time, I am not so involved in this topic... but I can come back to it.
  

Applications to other domains

I had the opportunity to propose various extensions of my work to some other descriptions of systems such as

• Descriptor systems

  I am trying to find strict LMI-based conditions for robust stability of uncertain systems with uncertainty on the derivative matrices.

  Also, I am interested in the use of Descriptor LFT-based uncertainty for simplifying many robustness analyses.

  Associating descriptor forms and nD systems is probably of high interest to suitably model some physical plants... but also lead to complicated theoretical challenges with previously many definitions to introduce and motivate... Coming soon ?

• Sensorless control of a synchronous motor

  Few years ago, I collaborated with my colleague Erik Etien on the sensorless control of the synchronous motor, using possibly robust or insensitive observers. I am no longer involved in this topic.

• Establishment of control laws for muti-sources energy devices

  I started to collaborate with my colleague Slim Tnani on possible applications of some advanced automatic control techniques to improve the efficiency of some multi-source (renewable) energy plants.

Societal and economic impacts of my research (JOKE!!!)

Sense of a doubt!

Rich of a MBA, a PhD in sociology as well as a master in linguistics that I mysterioulsy forgot to mention in the first tab of this page, I am currently trying to answer this fundamental question to get funds. I am especially looking for the linguistic rules the word "societal" complies with.



Energy and money loss in Research (Joke? Not so sure)

I am currently leading a joint experiment with thousands of other researchers in France on the impact of our applications for funds. It is a very exciting new topic which has been continuously growing in importance in the wide community of researchers. The idea is very simple: We spend a large amount of time (and time is money!) as well as much energy to prepare sophisticated documents in order to get funds while being aware that the application is very unlikely to be successful. It has several major advantages:



• It wastes money in administrative procedures and staff, which is of crucial importance in a period where money is available in overabundance.

• It wastes energy but this is human energy so it has absolutely no impact on the climate change. Isn't it marvelous to spend so much energy but not to contribute to the future floods? By creating a system which consumes so much energy to produce almost nothing, we give insights into (if not pave the way to) the creation, one day, of a kind of reverse system which would consume very little energy for a huge effect. This is maybe what some clever decision makers have bet on.

• It prevents us from doing research and thus from falling in deep addiction to science.

• The above-mentioned loss of energy and time(=money) has actually a kind of retroactive effect: Indeed, think about all the time all those researchers spent studying tough scientific disciplines. This investment is no longer exploited. This is just magic! Not only the currently supplied energy is wasted but also the past one. This is a NON CAUSAL feedback control law, i.e. a phenomenum that many scientists whould have thought impossible.

• While chasing new funds, we write long texts on the economic impacts of our non existing research on the markets. It has a double interest: It gives us the opportunity to write on something we just don't know at all and moreover, someone else will read it. This is what is called SYNERGY. The time you loose can be lost again by someone else. Magic once again!

• As all these applications are time-consuming (so nice, really!), they also prevent us from improving our teaching documents and methods. So the benefits go far beyond the research world, it has a non negligible impact on the quality of the teachings. The students will soon thank us for that.

• We have now hundreds of versions of ours CVs (one page, two pages, four pages with font size 11pt, half a line, two hundred pages, 143.5 block capitals and so on).

• Last but not least. To test the robustness of such a system to disturbances, few applications are successful, hence they swallow a large amount of money, fortunately only leaving a very weak fraction to the majority of researchers who do not suffer from this arrival of money. The magic is that - yes! - the system is robust. Nevertheless, to avoid a broad geographical distribution of the victims, the money attacks (disturbances) are only performed in large cities, large universities, where people are already very used to face such events. It is a very subtle and gently way to impoverish some regions in which some non educated people could have a vague desire to study science and do research (Oh my God!) whereas they should stay in their caves.

• Unfortunately, in spite of those laudable efforts to consume the researchers' time, some of them, seditious rebels, go on doing research and sharing science. To control part of this sedition, a new fantastic idea has been implemented. It relies on the fact that researchers are sometimes also teachers. Therefore, it they still can find time to do research, it becomes highly necessary to make them busier with their teachings. However, by teaching, they could contribute to spread science what would be very dangerous. So, more subtly, they should be overwhelmed by collateral tasks related to teachings. Hence marvelous reforms such as the reform of IUT, to transform the "Diplôme Universitaire de Technologie" into the "Bachelor Universitaire de Technologie" (thus introducing an English word in a French expression, like when clever people speak in reality shows (e.g. "C'est la life !"). Such reforms can be accompanied by abstruse pedagogic theory and language which recently revealed very efficient to "destroy" the high schools and many others establishments. Once again, it has a double impact: It consumes huge energy and time from the researchers and it prevents them from suitably educating students who could inadvertendly becomes new researchers.

For all these reasons, I am so much enthusiastic about the evolution of research in my country.

FINALLY, UNLIKE WHAT IS CLAIMED ABOVE, THIS IS THE TOPIC I'M THE MOST INVOLVED IN!

It's a kind of magic... (Freddy Mercury)