Finite‐time estimation for a class of systems with unknown time‐delay using modulating functions‐based method

Abstract

AbstractTime‐delay systems are widely used to model real problems. Most of the works on such systems assume prior knowledge of the delay, which is mostly unknown in real applications. This paper aims to fast and robustly estimate unknown delay, parameters, and output derivatives for a class of linear time‐delay systems in noisy environment. First, the classical modulating functions method is combined with the recursive least square algorithm and the Gauss–Newton method to estimate the coefficients and the time‐delay, respectively. Second, the generalized modulating functions method is adopted to provide algebraic integral formulas to estimate the output derivatives using the estimated parameters. Finally, numerical simulations are given to demonstrate the efficiency and robustness of the proposed methods.