Finite‐Dimensional Adaptive Observer Design for Reaction Diffusion Equation With Large Output Delay

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ABSTRACTThe goal of this paper is to present a new finite‐dimensional adaptive observer for some uncertain linear parabolic systems with delayed measurements. The observer is based on the modal decomposition approach and uses a classical persistent excitation condition. We prove that by using a finite‐dimensional state predictor, we ensure exponential convergence of both states parameters estimation error for arbitrary long constant delay.