Delay and state observer for SISO LTI systems

This paper deals with the problem of state and delay estimation for SISO LTI systems, with unknown time-varying delay in the input. Thanks to an adequate approximation of the delayed input by the Taylor´s theorem, an original approach based on observer design is proposed in order to estimate both state and delay. This new technique allows the estimation of time-varying delay. The convergence of the observer is formally proved. The efficiency of the method is widely illustrated by simulations.