State estimation for nonlinear systems with delayed output measurements

In this paper, we consider the problem of state estimation for nonlinear systems when the output measurements are delayed. We assume an observer is available that takes the delayed outputs and estimates the delayed states of the system. We propose a novel predictor that takes the delayed estimates from the observer and fuses them with the current input measurements of the system to compensate for the delay. We provide a rigorous stability analysis for globally Lipschitz systems demonstrating that the prediction of the system state converges (asymptotically/exponentially) to the current system trajectory if the observer state converges (asymptotically/exponentially) to the delayed system state. The predictor is computationally simple as it is recursively implementable with a set of delay differential equations. We demonstrate the performance of the proposed predictor via simulation studies.