Observer design for a class of uncertain systems with delayed outputs

International audienceIn this paper, a state observer is proposed for a class of nonlinear systems in the presence of uncertainties in the state equations and an arbitrarily long delay in the output. The proposed predictor has a cascade structure in such a way that the first system in the cascade allows to estimate the delayed state while each of the remaining ones is an appropriate predictor. Each predictor estimates the state of the preceding one with a prediction horizon equal to a fraction of the time delay in such a way that the state of the last predictor is an estimate of the system actual state. The design of the observer is achieved by assuming a set of conditions under which the ultimate boundedness of the estimation error is established. More specifically it is shown that the asymptotic observation error remains in a ball which radius particularly depends on the magnitudes of the delay and the Lipschitz constant of the system nonlinearities. Of primary importance, it is proven that the observation error converges exponentially to zero in the absence of uncertainties. Simulations results are given in order to illustrate the performance and the main properties of the proposed observer