Issues in separable identification of continuous-time models with time-delay

This paper discusses several issues related to the identification of time-delayed continuous-time systems using the refined instrumental variable method. The proposed estimation procedure is iterative where, at each iteration, the rational system parameters and time-delay are estimated separately. The main contribution of this paper covers three aspects. Firstly, conditions for persistent excitation are established, which should be satisfied to guarantee the identifiability of the system parameters and time-delay. Secondly, existence of multiple minima in the loss function is investigated. Due to the nonlinear nature of the loss function to be optimized with respect to the time-delay, initialization is a particularly important issue for correct estimation of the time-delay. Lastly, to reliably initialize the identification algorithm, based on the previous analysis, some guidelines are proposed to facilitate the choice of reliable initial parameters. The main results derived in this paper are verified by means of both theoretical analyses and numerical simulations.