Ph.D. student under the direction of

**F. LAMNABHI-LAGARRIGUE****Thesis title:**Sample data observers with time-varying gain for a large class of nonlinear systems

**Thesis abstract:**The control and observation of systems called Networked control systems (NCSs) are currently attracting a lot of attention in the control community. In many applications, the interest for NCSs is motivated by many advantages they offer such as the ease of maintenance and installation, the greater flexibility and the low cost. For these reasons, many industrial control applications use a serial communication channel to connect sensors and controllers. In NCSs, the serial communication channel has many nodes (sensors and actuators) but the signals of these nodes cannot be transmitted at the same time. The rule that selects which node will use the network to transmit its data, is called scheduling network protocol. It is well known that the stability of these systems is largely determined by the transmission protocol used and by the so-called maximum allowable transfer interval (MATI), i.e., the maximum allowable time between any two successive transmissions in the network. Enlarging the sampling intervals in the networked control/estimation is a hot topic [1, 2]. In a recent paper [3] it was shown that a time-varying gain improves the exponential convergence of the observer in the presence of the measurement delay. In our group, we recently shown, by combining results from [3] and [4] that using a time varying gain for some classes of nonlinear sampled-data systems, in the presence of the measurement delay, allows to enlarge significantly the sampling intervals that preserve the stability. We derived sufficient conditions described by some Linear Matrixes Inequalities which involve both the parameter and the bound of the maximum allowable sampling interval. The subject of this thesis will be to use this recent work for larger classes of systems (those of [5] for instance) and to show that the introduction of the above time varying gain can significantly enlarge the bound on the sampling intervals compared to constant gain cases.