Parameter estimation algorithms of linear systems with time-delays based on the frequency responses and harmonic balances under the multi-frequency sinusoidal signal excitation

In this paper, we study the parameter estimation problem of a class of linear time-delay systems. Based on the frequency responses and harmonic balance methods and by means of the gradient search, a two-stage stochastic gradient and gradient-based iterative algorithm is developed by using the collected data under the sinusoidal excitation. To improve the estimation accuracy, a two-stage multi-innovation stochastic gradient and gradient-based iterative algorithm is presented. Two simulation examples are provided to test the proposed algorithms.