Cascade observer for a class of nonlinear systems with output delays

This paper proposes a state observer with a cascade structure for a class of nonlinear systems in the presence of delayed output measurements. The first system in the cascade allows to estimate the delayed state while each of the remaining ones is a 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 exponential convergence of the estimation error to zero is established, namely the system is uniformly observable for any any input and its nonlinearities are globally Lipschitz. Of particular interest, it is shown that the number of the systems in the cascade depends on the magnitudes of the considered delay and the Lipschitz constant. The performance of the proposed observer and its main properties are compared with those of two existing observers through a typical bioreactor model.