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International audience; We propose a new design for a repetitive control scheme for nonlinear minimum-phase systems with arbitrary relative degree and globally Lipschitz nonlinearities. We represent the delay of the repetitive control scheme as a transport equation and we propose a new forwarding-based (partial) state-feedback design that uses not only the boundary information of the delay, but the entire state of the transport equation representing the delay. Through a rigorous mathematical analysis, we show that, from a theoretical point of view, asymptotic convergence of the desired regulated output can be achieved with the proposed control design.

International audience; We consider the problem of state observation for systems having a well-defined observability canonical form (Gauthier and Kupka (2004)) by means of high-gain observers. The main goal is to show that, for this class of systems, observers can be designed with the high-gain parameter powered just up to the order 2 regardless the dimension of the state system. In this way we substantially overtake the main limitations of standard design procedures in which the high-gain parameter is powered up to the order of the system. The observer structure, which generalizes the ideas presented in Astolfi and Marconi (2015), can be used in all those contexts where fast state observation is required, such as in the design of output feedback stabilizers by means of the nonlinear separation principle that is also specifically addressed in the paper.