Delay identification for a class of nonlinear systems

The problem of state estimation for nonlinear systems with unknown state delays is still an open problem. In this paper, we propose to add a delay identifier to suitable high-gain observers in order to achieve simultaneous estimation of state and delay. In the case of one constant delay in the state, we provide sufficient conditions to guarantee the exponential convergence to zero of the errors, globally with respect to the initial choice of the system state variables and locally with respect to the initial delay estimation. We validate the method through an example concerning chaotic oscillators.