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The design of observers for nonlinear systems with unknown, time-varying, bounded delays, on both state and input, still constitutes an open problem. In this paper, we show how to solve it for a class of nonlinear systems by combining the high gain observer approach with a Lyapunov-Krasovskii functional suitable choice. Sufficient conditions are provided to prove the practical stability of the observer. It is shown that the observation error is bounded and depends on the size of two parameters: the known upper bound delay of the unknown time-varying function delay and the instantaneous state dynamic variation. Furthermore, for the particular case of constant known time delay, the convergence of the proposed observer becomes exponential. The feasibility of the proposed strategy is illustrated by a numerical example.

International audienceIt is well-known that standard predictive techniques are not very robust to parameter uncertainties and to external disturbances. Furthermore, they require the exact knowledge of the delay. In practice, these constraints are rarely satisfied. In this paper, solutions are presented to allow the use of predictive control in presence of external disturbances, parameter uncertainties and an unknown input delay. First, a recent predictive control method developed to attenuate the effect of external disturbances is shown to be also robust to parameter uncertainties. In addition, a delay estimator is presented to estimate unknown time-varying delays. Theoretical results are widely illustrated through experimental tests on a DC motor

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