This paper investigates the robust H∞ estimation problem for a class of 2D FMLSS systems under asynchronous multi-channel delays. We overcame the substantial challenges caused by incomplete information due to external random perturbation and multi-channel delay. First, by employing partition reconstruction approach, the original delayed systems is transformed into an equivalent multi-channel observation delay-free systems. Then, by making two modifications to the quadratic performance function, an equivalence relation is established between the design of the H∞ filter and a minimization problem of an indefinite quadratic form. i) the first modification involves adding a random perturbation matrix term to the quadratic performance function, ensuring that the perturbation is simultaneously considered when the original system is dualized in line with the quadratic performance function; ii) the second modification replaces the initial observation and noise sequences in the quadratic performance function with reconstructed observation and noise sequences. This ensures the completeness of information in the estimation algorithm during real-time recursive computation. Then, an N-step robust H∞ filter is designed in the 2D Krein space stochastic system, and the necessary and sufficient conditions for its existence are provided. Finally, the effectiveness of the proposed recursive filtering algorithm is verified through a numerical example.
Chen et al. (Wed,) studied this question.