Online identification of time‐varying delay systems under relaxed input conditions

Identification of time delay is a prerequisite for the realisation of control compensation. The existing researches generally assume that the system input should be monotonic, which is unsuitable for online identification due to system saturation. To solve this problem, relaxed input conditions are developed in this Letter. Then a modified least‐square algorithm with forgetting factors, which has a strong ability in tracking time‐varying delays, is presented. Meanwhile, two extra terms whose design parameters are adjusted online according to the input condition are added into the covariance update law to guarantee the boundedness and robustness of the algorithm. Simulation results demonstrate the superiority of the proposed method and the reasonableness of the developed input conditions.