Online identification method for a system with unknown varying time-delay and parameter

An online identification method that can simultaneously estimate the unknown system parameter and the unknown time-delay is proposed. Firstly, with the help of Lagrange mean value theorem, the system with time-delay can be transformed into two terms that can be identified by modified least-square algorithm and one term that represents an approximate error. Then, a modified least-square algorithm is introduced to estimate all the unknown parameters in case of external disturbances. Additionally, an restrain term are added in the covariance matrix to enhance the robustness to deal with the approximate error which is related to the estimated error of system parameter and time-delay. Also, the boundedness of the estimation error is guaranteed via Lyapunov stability theory. Finally, the effectivity of the proposed method is verified by simulations results.