An asymptotic state observer for a class of nonlinear delay systems

The problem of state reconstruction from input and output measurements for nonlinear time delay systems is studied in this paper and a state observer is proposed that is easy to implement and, under suitable assumptions on th e system and on the input function, gives exponential observation error dec ay. The proposed observer is itself a delay system and can be classified as an identity observer, in that it is such that if at a given time instant t he system and observer states coincide, on a suitable Hilbert space, the ob servation error remains zero in all following time instants. The computatio n of the observer gain is straightforward. Computer simulations are reporte d that show the good performance of the observer.