Section: New Results

Time-delay systems

Participants : Jean-Pierre Richard, Lotfi Belkoura, Kaouther Ibn Taarit.

As it has been seen in the introductory example of subsection 3.1.5 , the framework of convolution equations can be used for fast identification issues and leads to computations analogous to the algebraic framework (multiplications by t and integrations). This link was pointed out for the first time in our communication: "Online identification of systems with delayed inputs" [75] . Further works have extended this first result, in particular a paper in Automatica [15] . This paper also introduced structured entries, such as discontinuities, as another field of application for the same techniques. This first step now allows for the investigation of systems with switches and, in particular, systems with dry friction.

Among the many applications of time-delay systems, note they constitute a basic tool for modelling systems controlled over communication networks. During the year 2009, we improved and implemented our results on Master-Slave control with Internet-in-the-loop. The idea was to develop an observer that enables the Master to estimate the present state of the Slave despite the variable communication delays and packet losses coming from the network. This technique has now been implemented (remote control of a light mobile robot, with poor computation power, through Internet and Blutooth connections). The control algorithms have been improved so that the controller can adapt his gains to the available quality of service (QoS) of the network [55] , [56] , [57] , [72] .