Ph.D. student under the direction of

**D. NORMAND-CYROT****Thesis title:**Observer design for nonlinear systems under sampling

**Thesis abstract:**In control theory, great attention has been always addressed to the observation at large. This topic is of paramount interest because, usually, feedback design relies upon the necessity of measuring the state although practical limitations from both economical and practical issues prevent from the installation of the required sensors. Based on this, the problem of reconstructing the state of a given plant starting from the available measures of the outputs has been widely investigated in the modern literature. In the linear case, a general result has been provided by the celebrated Luenberger observer in 1971. When dealing with nonlinear systems, a general structure for the observer is not generally available as one should face a trade off among the computational difficulties (usually arising with PDEs to be solved) and the large variety of dynamics which one might encounter. In this sense, usually, quite general observers can be built while yielding local convergence to the actual state of the system. When local properties are not enough, the design of the observer might proceed by an ad-hoc procedure that keeps into account the nature of the plant to reconstruct. Moreover, most of the works on these topics have been addressing the problem when assuming measures available at any time-instant. Though, this scenario is not satisfactory and realistic as most of sensors are digital and provide information on the plant only at sporadic time instants. This enlarges the problem to the sampled-data context where things get even more complicated when assuming the control feedback implemented through sample-and-hold devices. This opens a wide number of questions which deal with two main points: the reconstruction of the state of a given system based on sampled-data measures; the feedback design under sampled-measures and sample-and-hold devices for the implementation of the control action.