Joint state estimation and delay identification for nonlinear systems with delayed measurements

The problem of state estimation for nonlinear systems with unknown state or measurement delays is still an open problem. Inthis paper we consider the case of measurement delay and proposean approach that combines a delay identifier with a suitable highgainobserver in order to achieve simultaneous estimation of state anddelay. We provide sufficient conditions that guarantee the exponentialconvergence to zero of the errors, globally with respect to the systemvariables and locally with respect to the delay estimation. We validatethe method through an example concerning population models.