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Observer‐based Fault Estimators Using Iterative Learning Scheme for Linear Time‐delay Systems with Intermittent Faults

This paper deals with the fault estimation problem for a class of linear time‐delay systems with intermittent fault and measurement noise. Different from existing observer‐based fault estimation schemes, in the proposed design, an iterative learning observer is constructed by using the integrated errors composed of state predictive error and tracking error in the previous iteration. First of all, Lyapunov function including the information of time delay is proposed to guarantee the convergence of system output. Subsequently, a novel fault estimation law based on iterative learning scheme is presented to estimate the size and shape of various fault signals. Upon system output convergence analysis, we proposed an optimal function to select appropriate learning gain matrixes such that tracking error converges to zero, simultaneously to ensure the robustness of the proposed iterative learning observer which is influenced by measurement noise. Note that, an improved sufficient condition for the existence of such an estimator is established in terms of the linear matrix inequality (LMI) by the Schur complements and Young relation. In addition, the results are both suit for the systems with time‐varying delay and the systems with constant delay. Finally, three numerical examples are given to illustrate the effectiveness of the proposed methods and two comparability examples are provided to prove the superiority of the algorithm.